TESTING.asciidoc fix examples using forbidden annotation (#34515)

Clean up examples not to use forbidden test annotation `@Nightly`.
remove references to unused annotations

TESTING.asciidoc

@@ -77,39 +77,24 @@ Run a single test case (variants)
 ./gradlew test "-Dtests.class=*.ClassName"
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-Run all tests in a package and sub-packages
+Run all tests in a package and its sub-packages
 
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 ./gradlew test "-Dtests.class=org.elasticsearch.package.*"
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-Run any test methods that contain 'esi' (like: ...r*esi*ze...).
+Run any test methods that contain 'esi' (like: ...r*esi*ze...)
 
 -------------------------------
 ./gradlew test "-Dtests.method=*esi*"
 -------------------------------
 
-You can also filter tests by certain annotations ie:
-
-  * `@Nightly` - tests that only run in nightly builds (disabled by default)
-  * `@Backwards` - backwards compatibility tests (disabled by default)
-  * `@AwaitsFix` - tests that are waiting for a bugfix (disabled by default)
-  * `@BadApple` - tests that are known to fail randomly (disabled by default)
-
-Those annotation names can be combined into a filter expression like:
+Run all tests that are waiting for a bugfix (disabled by default)
 
 ------------------------------------------------
-./gradlew test -Dtests.filter="@nightly and not @backwards"
+./gradlew test -Dtests.filter=@awaitsfix
 ------------------------------------------------
 
-to run all nightly test but not the ones that are backwards tests. `tests.filter` supports
-the boolean operators `and, or, not` and grouping ie:
-
-
----------------------------------------------------------------
-./gradlew test -Dtests.filter="@nightly and not(@badapple or @backwards)"
----------------------------------------------------------------
-
 === Seed and repetitions.
 
 Run with a given seed (seed is a hex-encoded long).
@@ -160,8 +145,6 @@ Test groups can be enabled or disabled (true/false).
 Default value provided below in [brackets].
 
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-./gradlew test -Dtests.nightly=[false]   - nightly test group (@Nightly)
-./gradlew test -Dtests.weekly=[false]    - weekly tests (@Weekly)
 ./gradlew test -Dtests.awaitsfix=[false] - known issue (@AwaitsFix)
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