diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 8922f604e..95a63ba45 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -212,7 +212,7 @@ jobs:
           ./Build/Scripts/runTests.sh -p ${{ matrix.php-version }} -t ${{matrix.typo3-version}} -s composerUpdate${{matrix.composer-dependencies}}
       - name: Run unit tests
         run: |
-          ./Build/Scripts/runTests.sh -p ${{ matrix.php-version }} -s unit
+          ./Build/Scripts/runTests.sh -p ${{ matrix.php-version }} -t ${{matrix.typo3-version}} -s unit
     strategy:
       fail-fast: false
       matrix:
@@ -263,7 +263,7 @@ jobs:
           ./Build/Scripts/runTests.sh -p ${{ matrix.php-version }} -t ${{matrix.typo3-version}} -s composerUpdate${{matrix.composer-dependencies}}
       - name: Run functional tests
         run: |
-          ./Build/Scripts/runTests.sh -p ${{ matrix.php-version }} -d ${{ matrix.dbms }} -s functional
+          ./Build/Scripts/runTests.sh -p ${{ matrix.php-version }} -t ${{matrix.typo3-version}} -d ${{ matrix.dbms }} -s functional
     strategy:
       fail-fast: false
       matrix:
diff --git a/Build/Scripts/runTests.sh b/Build/Scripts/runTests.sh
index 3f2a30359..2bb8b3bfe 100755
--- a/Build/Scripts/runTests.sh
+++ b/Build/Scripts/runTests.sh
@@ -1,5 +1,5 @@
 #!/usr/bin/env bash
-# shellcheck disable=SC2086,SC2046,SC2128,SC2178,SC2206
+# shellcheck disable=SC2086,SC2046,SC2128,SC2178,SC2206,SC2054
 
 # Uncomment for debugging
 # set -x
@@ -599,7 +599,7 @@ case ${TEST_SUITE} in
         SUITE_EXIT_CODE=$?
         ;;
     functional)
-        COMMAND=(.Build/bin/phpunit -c Build/phpunit/FunctionalTests.xml --exclude-group not-${DBMS} "$@")
+        COMMAND=(.Build/bin/phpunit -c Build/phpunit/FunctionalTests.xml --exclude-group not-${DBMS},not-core-${CORE_VERSION} "$@")
         case ${DBMS} in
             mariadb)
                 echo "Using driver: ${DATABASE_DRIVER}"
@@ -712,11 +712,11 @@ case ${TEST_SUITE} in
         SUITE_EXIT_CODE=$?
         ;;
     unit)
-        ${CONTAINER_BIN} run ${CONTAINER_COMMON_PARAMS} --name unit-${SUFFIX} ${XDEBUG_MODE} -e XDEBUG_CONFIG="${XDEBUG_CONFIG}" ${IMAGE_PHP} .Build/bin/phpunit -c Build/phpunit/UnitTests.xml "$@"
+        ${CONTAINER_BIN} run ${CONTAINER_COMMON_PARAMS} --name unit-${SUFFIX} ${XDEBUG_MODE} -e XDEBUG_CONFIG="${XDEBUG_CONFIG}" ${IMAGE_PHP} .Build/bin/phpunit -c Build/phpunit/UnitTests.xml --exclude-group not-core-${CORE_VERSION} "$@"
         SUITE_EXIT_CODE=$?
         ;;
     unitRandom)
-        ${CONTAINER_BIN} run ${CONTAINER_COMMON_PARAMS} --name unit-random-${SUFFIX} ${XDEBUG_MODE} -e XDEBUG_CONFIG="${XDEBUG_CONFIG}" ${IMAGE_PHP} .Build/bin/phpunit -c Build/phpunit/UnitTests.xml --order-by=random ${PHPUNIT_RANDOM} "$@"
+        ${CONTAINER_BIN} run ${CONTAINER_COMMON_PARAMS} --name unit-random-${SUFFIX} ${XDEBUG_MODE} -e XDEBUG_CONFIG="${XDEBUG_CONFIG}" ${IMAGE_PHP} .Build/bin/phpunit -c Build/phpunit/UnitTests.xml --exclude-group not-core-${CORE_VERSION} --order-by=random ${PHPUNIT_RANDOM} "$@"
         SUITE_EXIT_CODE=$?
         ;;
     update)
diff --git a/Tests/Functional/Environment/ExtensionTest.php b/Tests/Functional/Environment/ExtensionTest.php
deleted file mode 100644
index 3ca1b5752..000000000
--- a/Tests/Functional/Environment/ExtensionTest.php
+++ /dev/null
@@ -1,25 +0,0 @@
-<?php
-
-declare(strict_types=1);
-
-namespace TTN\Tea\Tests\Functional\Environment;
-
-use PHPUnit\Framework\Attributes\CoversNothing;
-use PHPUnit\Framework\Attributes\Test;
-use TYPO3\CMS\Core\Utility\ExtensionManagementUtility;
-use TYPO3\TestingFramework\Core\Functional\FunctionalTestCase;
-
-#[CoversNothing]
-final class ExtensionTest extends FunctionalTestCase
-{
-    protected array $testExtensionsToLoad = ['ttn/tea'];
-    protected bool $initializeDatabase = false;
-
-    #[Test]
-    public function isLoaded(): void
-    {
-        self::assertTrue(
-            ExtensionManagementUtility::isLoaded('tea')
-        );
-    }
-}
diff --git a/Tests/Functional/ExtensionLoadedTest.php b/Tests/Functional/ExtensionLoadedTest.php
new file mode 100644
index 000000000..a1cffc8ed
--- /dev/null
+++ b/Tests/Functional/ExtensionLoadedTest.php
@@ -0,0 +1,62 @@
+<?php
+
+declare(strict_types=1);
+
+namespace TTN\Tea\Tests\Functional;
+
+use PHPUnit\Framework\Attributes\CoversNothing;
+use PHPUnit\Framework\Attributes\Group;
+use PHPUnit\Framework\Attributes\Test;
+use TYPO3\CMS\Core\Information\Typo3Version;
+use TYPO3\CMS\Core\Utility\ExtensionManagementUtility;
+use TYPO3\TestingFramework\Core\Functional\FunctionalTestCase;
+
+/**
+ * Basic unit tests.
+ *
+ * This can and should be used in every extension instead of dummy assertTrue(true) filler.
+ * This checks against supported version and additional ensures that the test execution is
+ * using the same core version installed, which can help to rule out other test failures
+ * early due to wrong TYPO3 version usage.
+ */
+#[CoversNothing]
+final class ExtensionLoadedTest extends FunctionalTestCase
+{
+    private const ALLOWED_MAJOR_VERSIONS = [12, 13];
+
+    protected array $testExtensionsToLoad = [
+        'ttn/tea',
+    ];
+
+    #[Test]
+    public function isLoadedExtensionKey(): void
+    {
+        self::assertTrue(ExtensionManagementUtility::isLoaded('tea'));
+    }
+
+    #[Test]
+    public function isLoadedComposerPackageName(): void
+    {
+        self::assertTrue(ExtensionManagementUtility::isLoaded('ttn/tea'));
+    }
+
+    #[Test]
+    public function allowedMajorTypo3Version(): void
+    {
+        self::assertContains((new Typo3Version())->getMajorVersion(), self::ALLOWED_MAJOR_VERSIONS);
+    }
+
+    #[Group('not-core-13.4')]
+    #[Test]
+    public function verifyCore12(): void
+    {
+        self::assertSame(12, (new Typo3Version())->getMajorVersion());
+    }
+
+    #[Group('not-core-12.4')]
+    #[Test]
+    public function verifyCore13(): void
+    {
+        self::assertSame(13, (new Typo3Version())->getMajorVersion());
+    }
+}
diff --git a/Tests/Unit/Environment/ExtensionTest.php b/Tests/Unit/Environment/ExtensionTest.php
deleted file mode 100644
index e2bc4bbc2..000000000
--- a/Tests/Unit/Environment/ExtensionTest.php
+++ /dev/null
@@ -1,25 +0,0 @@
-<?php
-
-declare(strict_types=1);
-
-namespace TTN\Tea\Tests\Unit\Environment;
-
-use PHPUnit\Framework\Attributes\CoversNothing;
-use PHPUnit\Framework\Attributes\Test;
-use TYPO3\CMS\Core\Information\Typo3Version;
-use TYPO3\TestingFramework\Core\Unit\UnitTestCase;
-
-#[CoversNothing]
-final class ExtensionTest extends UnitTestCase
-{
-    #[Test]
-    public function currentVersionIsSupported(): void
-    {
-        $supportedVersions = [12, 13];
-        $currentVersion = (new Typo3Version())->getMajorVersion();
-        self::assertContains(
-            $currentVersion,
-            $supportedVersions
-        );
-    }
-}
diff --git a/Tests/Unit/VersionCompatTest.php b/Tests/Unit/VersionCompatTest.php
new file mode 100644
index 000000000..b3ffb4f99
--- /dev/null
+++ b/Tests/Unit/VersionCompatTest.php
@@ -0,0 +1,42 @@
+<?php
+
+declare(strict_types=1);
+
+namespace TTN\Tea\Tests\Unit;
+
+use PHPUnit\Framework\Attributes\CoversNothing;
+use PHPUnit\Framework\Attributes\Group;
+use PHPUnit\Framework\Attributes\Test;
+use TYPO3\CMS\Core\Information\Typo3Version;
+use TYPO3\TestingFramework\Core\Unit\UnitTestCase;
+
+/**
+ * Basic unit tests.
+ *
+ * This can and should be used in every extension instead of dummy assertTrue(true) filler.
+ */
+#[CoversNothing]
+final class VersionCompatTest extends UnitTestCase
+{
+    private const ALLOWED_MAJOR_VERSIONS = [12, 13];
+
+    #[Test]
+    public function allowedMajorTypo3Version(): void
+    {
+        self::assertContains((new Typo3Version())->getMajorVersion(), self::ALLOWED_MAJOR_VERSIONS);
+    }
+
+    #[Group('not-core-13.4')]
+    #[Test]
+    public function verifyCore12(): void
+    {
+        self::assertSame(12, (new Typo3Version())->getMajorVersion());
+    }
+
+    #[Group('not-core-12.4')]
+    #[Test]
+    public function verifyCore13(): void
+    {
+        self::assertSame(13, (new Typo3Version())->getMajorVersion());
+    }
+}
diff --git a/composer.json b/composer.json
index 35d2069a6..6105a28c5 100644
--- a/composer.json
+++ b/composer.json
@@ -123,7 +123,7 @@
 		"check:coverage:functional": [
 			"@check:tests:create-directories",
 			"@coverage:create-directories",
-			"phpunit -c Build/phpunit/FunctionalTests.xml --coverage-php=build/coverage/functional.cov"
+			"phpunit -c Build/phpunit/FunctionalTests.xml --exclude-group not-core-13.4 --coverage-php=build/coverage/functional.cov"
 		],
 		"check:coverage:merge": [
 			"@coverage:create-directories",
@@ -131,7 +131,7 @@
 		],
 		"check:coverage:unit": [
 			"@coverage:create-directories",
-			"phpunit -c Build/phpunit/UnitTests.xml --coverage-php=build/coverage/unit.cov"
+			"phpunit -c Build/phpunit/UnitTests.xml --exclude-group not-core-13.4 --coverage-php=build/coverage/unit.cov"
 		],
 		"check:json:lint": "find . ! -path '*/.cache/*' ! -path '*/.Build/*' ! -path '*/node_modules/*' -name '*.json' | xargs -r php .Build/bin/jsonlint -q",
 		"check:php": [