Cleanup multi-team docs for team_name tagging

[Tegh25]

As discussed in PR #69943, the unrelated doc changes are being moved to their own branch + PR instead of being attached to the other changes.

Relevant issue: #68294

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Was generative AI tooling used to co-author this PR?

• Yes (please specify the tool below)

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• Read the Pull Request Guidelines for more information. Note: commit author/co-author name and email in commits become permanently public when merged.
• For fundamental code changes, an Airflow Improvement Proposal (AIP) is needed.
• When adding dependency, check compliance with the ASF 3rd Party License Policy.
• For significant user-facing changes create newsfragment: {pr_number}.significant.rst, in airflow-core/newsfragments. You can add this file in a follow-up commit after the PR is created so you know the PR number.

[Tegh25]

@ferruzzi tagging you for visibility. Please review when you get the chance 🙂

[ferruzzi]

Ah, I just meant to move out the docs that weren't directly related to that PR. There were two that you updated because you saw they were wrong while you were in there.

The connection tests bullet and the scheduler.executor_heartbeat_duration / triggers.blocked_main_thread additions to the existing triggerer/executor bullets were directly related to that PR and should have stayed.

[Tegh25]

Thanks for the feedback. I amended the commit, should be correct now.

[ferruzzi]

Approved pending CI passing