diff --git a/composer.json b/composer.json
index 17f53c2116f71..649a3d429324c 100644
--- a/composer.json
+++ b/composer.json
@@ -23,7 +23,7 @@
 		"squizlabs/php_codesniffer": "3.13.5",
 		"wp-coding-standards/wpcs": "~3.3.0",
 		"phpcompatibility/phpcompatibility-wp": "~2.1.3",
-		"phpstan/phpstan": "2.1.39",
+		"phpstan/phpstan": "2.1.40",
 		"yoast/phpunit-polyfills": "^1.1.0"
 	},
 	"config": {
diff --git a/phpstan.neon.dist b/phpstan.neon.dist
index e74e6ec1a441b..38dd9c63098d0 100644
--- a/phpstan.neon.dist
+++ b/phpstan.neon.dist
@@ -14,7 +14,7 @@ includes:
 
 parameters:
 	# https://phpstan.org/user-guide/rule-levels
-	level: 0
+	level: 1
 	reportUnmatchedIgnoredErrors: true
 
 	ignoreErrors:
@@ -34,3 +34,8 @@ parameters:
 			identifier: function.inner
 			path: src/wp-includes/canonical.php
 			count: 1
+
+		# Level 1:
+		- # These are too noisy at the moment.
+			identifier: variable.undefined
+			message: '#Variable \$[a-zA-Z0-9_]+ might not be defined\.#'
diff --git a/src/wp-admin/includes/class-custom-image-header.php b/src/wp-admin/includes/class-custom-image-header.php
index eb65605728062..2c0eb26c0fc9a 100644
--- a/src/wp-admin/includes/class-custom-image-header.php
+++ b/src/wp-admin/includes/class-custom-image-header.php
@@ -841,7 +841,7 @@ public function step_2() {
 			$file          = get_attached_file( $attachment_id, true );
 			$url           = wp_get_attachment_image_src( $attachment_id, 'full' );
 			$url           = $url[0];
-		} elseif ( isset( $_POST ) ) {
+		} else {
 			$data          = $this->step_2_manage_upload();
 			$attachment_id = $data['attachment_id'];
 			$file          = $data['file'];
diff --git a/src/wp-admin/includes/class-wp-filesystem-direct.php b/src/wp-admin/includes/class-wp-filesystem-direct.php
index a4b197c15229f..34862a661d321 100644
--- a/src/wp-admin/includes/class-wp-filesystem-direct.php
+++ b/src/wp-admin/includes/class-wp-filesystem-direct.php
@@ -19,10 +19,8 @@ class WP_Filesystem_Direct extends WP_Filesystem_Base {
 	 * Constructor.
 	 *
 	 * @since 2.5.0
-	 *
-	 * @param mixed $arg Not used.
 	 */
-	public function __construct( $arg ) {
+	public function __construct() {
 		$this->method = 'direct';
 		$this->errors = new WP_Error();
 	}
diff --git a/src/wp-includes/class-wpdb.php b/src/wp-includes/class-wpdb.php
index 23c865b87d817..60026dbdc5c16 100644
--- a/src/wp-includes/class-wpdb.php
+++ b/src/wp-includes/class-wpdb.php
@@ -2117,7 +2117,9 @@ public function parse_db_host( $host ) {
 	 * @since 3.9.0
 	 *
 	 * @param bool $allow_bail Optional. Allows the function to bail. Default true.
-	 * @return bool|void True if the connection is up.
+	 * @return bool Whether the connection is up. Exits when `$allow_bail` is true and the connection is down.
+	 *
+	 * @phpstan-return ( $allow_bail is true ? bool|never : bool )
 	 */
 	public function check_connection( $allow_bail = true ) {
 		// Check if the connection is alive.
diff --git a/src/wp-includes/functions.php b/src/wp-includes/functions.php
index 4b6330a697780..8bf46ef0b871f 100644
--- a/src/wp-includes/functions.php
+++ b/src/wp-includes/functions.php
@@ -3766,7 +3766,7 @@ function wp_nonce_ays( $action ) {
  * }
  * @return never|void Returns void if `$args['exit']` is false, otherwise exits.
  *
- * @phpstan-return ( $args['exit'] is false ? void : never )
+ * @phpstan-return ( $args is array{exit: false} ? void : never )
  */
 function wp_die( $message = '', $title = '', $args = array() ) {
 	global $wp_query;
@@ -5501,6 +5501,8 @@ function wp_ob_end_flush_all() {
  * @since 2.3.2
  *
  * @global wpdb $wpdb WordPress database abstraction object.
+ *
+ * @return never
  */
 function dead_db() {
 	global $wpdb;
diff --git a/tests/phpstan/base.neon b/tests/phpstan/base.neon
index 347c2198ae953..7bfe9d6eff3df 100644
--- a/tests/phpstan/base.neon
+++ b/tests/phpstan/base.neon
@@ -25,6 +25,8 @@ parameters:
 		- ALLOW_SUBDIRECTORY_INSTALL
 		- AUTH_SALT
 		- AUTOMATIC_UPDATER_DISABLED
+		- BACKGROUND_COLOR
+		- BACKGROUND_IMAGE
 		- COOKIEPATH
 		- CUSTOM_TAGS
 		- DISALLOW_FILE_EDIT
@@ -32,8 +34,13 @@ parameters:
 		- EMPTY_TRASH_DAYS
 		- ENFORCE_GZIP
 		- FORCE_SSL_LOGIN
+		- HEADER_IMAGE
+		- HEADER_IMAGE_HEIGHT
+		- HEADER_IMAGE_WIDTH
+		- HEADER_TEXTCOLOR
 		- MEDIA_TRASH
 		- MULTISITE
+		- NO_HEADER_TEXT
 		- NOBLOGREDIRECT
 		- SAVEQUERIES
 		- SCRIPT_DEBUG
@@ -105,6 +112,8 @@ parameters:
 			- ../../src/wp-includes/deprecated.php
 			- ../../src/wp-includes/ms-deprecated.php
 			- ../../src/wp-includes/pluggable-deprecated.php
+			# These files are currently pulled in from Gutenberg, but maybe not long-term. See <https://core.trac.wordpress.org/ticket/64393>.
+			- ../../src/wp-includes/build
 			# These files are sourced by wordpress/gutenberg in `tools/release/sync-stable-blocks.js`.
 			- ../../src/wp-includes/blocks
 			# Third-party libraries.
diff --git a/tests/phpstan/baseline.php b/tests/phpstan/baseline.php
index 646cbdbef630c..810d719f57b6a 100644
--- a/tests/phpstan/baseline.php
+++ b/tests/phpstan/baseline.php
@@ -1,3 +1,107 @@
 <?php declare(strict_types = 1);
 
-return [];
+$ignoreErrors = [];
+$ignoreErrors[] = [
+	'message' => '#^Variable \\$class in empty\\(\\) always exists and is always falsy\\.$#',
+	'identifier' => 'empty.variable',
+	'count' => 1,
+	'path' => __DIR__ . '/../../src/wp-admin/includes/class-wp-posts-list-table.php',
+];
+$ignoreErrors[] = [
+	'message' => '#^Variable \\$_POST in isset\\(\\) always exists and is not nullable\\.$#',
+	'identifier' => 'isset.variable',
+	'count' => 1,
+	'path' => __DIR__ . '/../../src/wp-admin/includes/media.php',
+];
+$ignoreErrors[] = [
+	'message' => '#^Variable \\$parent_file in empty\\(\\) always exists and is not falsy\\.$#',
+	'identifier' => 'empty.variable',
+	'count' => 1,
+	'path' => __DIR__ . '/../../src/wp-admin/themes.php',
+];
+$ignoreErrors[] = [
+	'message' => '#^Function twentyseventeen_edit_link invoked with 1 parameter, 0 required\\.$#',
+	'identifier' => 'arguments.count',
+	'count' => 1,
+	'path' => __DIR__ . '/../../src/wp-content/themes/twentyseventeen/template-parts/page/content-front-page-panels.php',
+];
+$ignoreErrors[] = [
+	'message' => '#^Function twentyseventeen_edit_link invoked with 1 parameter, 0 required\\.$#',
+	'identifier' => 'arguments.count',
+	'count' => 1,
+	'path' => __DIR__ . '/../../src/wp-content/themes/twentyseventeen/template-parts/page/content-front-page.php',
+];
+$ignoreErrors[] = [
+	'message' => '#^Function twentyseventeen_edit_link invoked with 1 parameter, 0 required\\.$#',
+	'identifier' => 'arguments.count',
+	'count' => 1,
+	'path' => __DIR__ . '/../../src/wp-content/themes/twentyseventeen/template-parts/page/content-page.php',
+];
+$ignoreErrors[] = [
+	'message' => '#^Function wp_cache_switch_to_blog_fallback invoked with 1 parameter, 0 required\\.$#',
+	'identifier' => 'arguments.count',
+	'count' => 1,
+	'path' => __DIR__ . '/../../src/wp-includes/cache-compat.php',
+];
+$ignoreErrors[] = [
+	'message' => '#^Variable \\$addl_path in empty\\(\\) always exists and is always falsy\\.$#',
+	'identifier' => 'empty.variable',
+	'count' => 1,
+	'path' => __DIR__ . '/../../src/wp-includes/canonical.php',
+];
+$ignoreErrors[] = [
+	'message' => '#^Variable \\$namespace in isset\\(\\) always exists and is not nullable\\.$#',
+	'identifier' => 'isset.variable',
+	'count' => 1,
+	'path' => __DIR__ . '/../../src/wp-includes/class-wp-block-parser.php',
+];
+$ignoreErrors[] = [
+	'message' => '#^Variable \\$block_type in empty\\(\\) always exists and is not falsy\\.$#',
+	'identifier' => 'empty.variable',
+	'count' => 1,
+	'path' => __DIR__ . '/../../src/wp-includes/class-wp-block-supports.php',
+];
+$ignoreErrors[] = [
+	'message' => '#^Variable \\$loader in isset\\(\\) always exists and is not nullable\\.$#',
+	'identifier' => 'isset.variable',
+	'count' => 1,
+	'path' => __DIR__ . '/../../src/wp-includes/class-wp-oembed.php',
+];
+$ignoreErrors[] = [
+	'message' => '#^Variable \\$search in empty\\(\\) always exists and is not falsy\\.$#',
+	'identifier' => 'empty.variable',
+	'count' => 1,
+	'path' => __DIR__ . '/../../src/wp-includes/class-wp-query.php',
+];
+$ignoreErrors[] = [
+	'message' => '#^Variable \\$status_type_clauses in empty\\(\\) always exists and is not falsy\\.$#',
+	'identifier' => 'empty.variable',
+	'count' => 1,
+	'path' => __DIR__ . '/../../src/wp-includes/class-wp-query.php',
+];
+$ignoreErrors[] = [
+	'message' => '#^Variable \\$deprecated in empty\\(\\) always exists and is always falsy\\.$#',
+	'identifier' => 'empty.variable',
+	'count' => 1,
+	'path' => __DIR__ . '/../../src/wp-includes/pluggable.php',
+];
+$ignoreErrors[] = [
+	'message' => '#^Variable \\$schema in empty\\(\\) is never defined\\.$#',
+	'identifier' => 'empty.variable',
+	'count' => 1,
+	'path' => __DIR__ . '/../../src/wp-includes/rest-api/endpoints/class-wp-rest-attachments-controller.php',
+];
+$ignoreErrors[] = [
+	'message' => '#^Variable \\$the_parent in empty\\(\\) always exists and is not falsy\\.$#',
+	'identifier' => 'empty.variable',
+	'count' => 1,
+	'path' => __DIR__ . '/../../src/wp-includes/taxonomy.php',
+];
+$ignoreErrors[] = [
+	'message' => '#^Variable \\$s in isset\\(\\) is never defined\\.$#',
+	'identifier' => 'isset.variable',
+	'count' => 1,
+	'path' => __DIR__ . '/../../src/wp-includes/template.php',
+];
+
+return ['parameters' => ['ignoreErrors' => $ignoreErrors]];
diff --git a/tests/phpstan/bootstrap.php b/tests/phpstan/bootstrap.php
index c87a26babf83d..77a597609270e 100644
--- a/tests/phpstan/bootstrap.php
+++ b/tests/phpstan/bootstrap.php
@@ -93,3 +93,12 @@
 define( 'FS_TIMEOUT', 1 );
 define( 'FS_CHMOD_DIR', 1 );
 define( 'FS_CHMOD_FILE', 1 );
+
+// Theme constants referenced in add_theme_support().
+define( 'NO_HEADER_TEXT', false );
+define( 'HEADER_IMAGE_WIDTH', 0 );
+define( 'HEADER_IMAGE_HEIGHT', 0 );
+define( 'HEADER_TEXTCOLOR', '' );
+define( 'HEADER_IMAGE', '' );
+define( 'BACKGROUND_COLOR', '' );
+define( 'BACKGROUND_IMAGE', '' );