(Git-6) Use new Git Backend in Entire auto_tick flow

[ytausch]

Description:

Building upon #3003, this replaces the remaining auto_tick logic to use the new git backend.
Notably, this PR ensures that the new backend is used for opening PRs and commenting on PRs.

Checklist:

• Pydantic model updated or no update needed

Cross-refs, links to issues, etc:

#3003 should be merged first.

[ytausch]

@0xbe7a I think this is worth reviewing, even with limited knowledge of the codebase

[codecov]

Codecov Report

Attention: Patch coverage is 92.77108% with 36 lines in your changes missing coverage. Please review.

Project coverage is 77.01%. Comparing base (621910b) to head (c37ea4f).
Report is 11 commits behind head on main.

Files with missing lines	Patch %	Lines
conda_forge_tick/auto_tick.py	15.78%	16 Missing ⚠️
conda_forge_tick/git_utils.py	88.98%	13 Missing ⚠️
tests/test_git_utils.py	98.00%	7 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #3004      +/-   ##
==========================================
+ Coverage   76.15%   77.01%   +0.86%     
==========================================
  Files         120      120              
  Lines       12942    13201     +259     
==========================================
+ Hits         9856    10167     +311     
+ Misses       3086     3034      -52     

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

[ytausch]

Matt, FYI: Bela is no longer mentoring me, therefore I ping @pavelzw for an additional review.

[beckermr]

I left some comments. One todo item is to search the code base for any functions you have removed to ensure they are not used anywhere else.

[ytausch]

Thank you! I just verified that no removed function is used in the regro or conda-forge organization via a quick GitHub search.

[beckermr]

We're seeing errors in pushing to repos with this so I am going to revert.