UI: Share one tooltip root across Dag card run-state badges

[yuseok89]

related: #69609

Each Dag card renders 4 run-state badges (added in #67242), each with its own Tooltip.Root. On a page of 50 cards that's up to 200 independent tooltip controllers, even though only one tooltip can be active at a time.

This applies the same pattern #69681 used for the recent-runs bar: one shared Tooltip.Root per card, with each badge as a Tooltip.Trigger, and the hovered badge's content resolved through Tooltip.Context. No visual change is expected.

Demo

Screen.Recording.2026-07-15.at.11.07.54.PM.mov

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[bbovenzi]

Thanks for helping with the dags list performance!

[github-actions]

Backport failed to create: v3-3-test. View the failure log Run details

Note: As of Merging PRs targeted for Airflow 3.X
the committer who merges the PR is responsible for backporting the PRs that are bug fixes (generally speaking) to the maintenance branches.

In matter of doubt please ask in #release-management Slack channel.

Status	Branch	Result
❌	v3-3-test

You can attempt to backport this manually by running:

cherry_picker 018f0c2 v3-3-test

This should apply the commit to the v3-3-test branch and leave the commit in conflict state marking
the files that need manual conflict resolution.

After you have resolved the conflicts, you can continue the backport process by running:

cherry_picker --continue

If you don't have cherry-picker installed, see the installation guide.

[pierrejeambrun]

Depends on #67242 marked for 3.4.0. Updating the milestone of this PR to 3.4.0 as well.