Run UI tests selectively

[ashb]

Closes #14957

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Read the Pull Request Guidelines for more information.
In case of fundamental code change, Airflow Improvement Proposal (AIP) is needed.
In case of a new dependency, check compliance with the ASF 3rd Party License Policy.
In case of backwards incompatible changes please leave a note in UPDATING.md.

[github-actions]

The Workflow run is cancelling this PR. It has some failed jobs matching ^Pylint$,^Static checks,^Build docs$,^Spell check docs$,^Provider packages,^Checks: Helm tests$,^Test OpenAPI*.

[github-actions]

The Workflow run is cancelling this PR. It has some failed jobs matching ^Pylint$,^Static checks,^Build docs$,^Spell check docs$,^Provider packages,^Checks: Helm tests$,^Test OpenAPI*.

[ashb]

Note that this PR will build everything as the CI scripts have changed.

[github-actions]

The PR most likely needs to run full matrix of tests because it modifies parts of the core of Airflow. However, committers might decide to merge it quickly and take the risk. If they don't merge it quickly - please rebase it to the latest master at your convenience, or amend the last commit of the PR, and push it with --force-with-lease.