[fix][CI] Fix auto merge action

[Andrews2024]

General:

Fixes the GHA to automatically merge main into gh-pages when a push is made to main. This will keep gh-pages and docs up to date.
The nightly merge GHA doesn't seem to have a lot of debugging options available, and it fails with merge conflicts where manually performing the merge locally has no issues. This PR scraps the nightly merge workflow for a series of git commands to make the merge.

Pull Request Guidelines:

1. Does your submission pass tests?
2. Are you addressing a single feature in this PR?
3. Are your commits atomic, addressing one change per commit?
4. Are you following the conventions of the language?
5. Have you saved your large formatting changes for a different PR, so we can focus on your work?
6. Have you explained your rationale for why this feature is needed?

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 72.98%. Comparing base (deb8ce8) to head (37e018f).
Report is 1 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main     #367   +/-   ##
=======================================
  Coverage   72.98%   72.98%           
=======================================
  Files          14       14           
  Lines        2599     2599           
=======================================
  Hits         1897     1897           
  Misses        537      537           
  Partials      165      165           

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