[AIP-94] Create a CLI airflowctl client and adopt it in existing commands

[bugraoz93]

closes: #64924

Deprecation of the local bespoke api client replaced with airflowctl.
Existing members are migrated.
This should enable migrating other commands easily.

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

• Yes (please specify the tool below)
  Claude Opus 4.8

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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.

[jscheffl]

One question: Was it not planned also to add a deprecation note that in future these commands will be removed and be an alias only? Would it be beneficial when switching to add the deprecation note early?

[bugraoz93]

One question: Was it not planned also to add a deprecation note that in future these commands will be removed and be an alias only? Would it be beneficial when switching to add the deprecation note early?

Great point Jens! Many thanks for the review! Will address this before merging :)

[bugraoz93]

Some of local tests

One question: Was it not planned also to add a deprecation note that in future these commands will be removed and be an alias only? Would it be beneficial when switching to add the deprecation note early?

Added with the airflowctl command replacement in the log to see and get used to them :)

[bugraoz93]

CI was green before rebase
Should be fixed in #68300

[bugraoz93]

UI go wrong and merged the changes rather rebase. I will rebase before merging. If no objection will merge today