Update the `publish_site` docs to unblock website deployment

[saitcakmak]

The existing publish_site script attempts to force-push to the gh-pages branch, which gets rejected due to gh-pages being a protected branch. This updates the script to modify the git repo in-place and use git push rather than force-push. The changes are based on the BoTorch script: https://github.com/pytorch/botorch/blob/main/scripts/publish_site.sh

Test plan: The workflow should successfully complete: https://github.com/facebook/Ax/runs/6086578017?check_suite_focus=true

[codecov-commenter]

Codecov Report

Merging #921 (54990c1) into main (c26fbf4) will not change coverage. The diff coverage is n/a.

@@           Coverage Diff           @@
##             main     #921   +/-   ##
=======================================
  Coverage   94.13%   94.13%           
=======================================
  Files         397      397           
  Lines       34140    34140           
=======================================
  Hits        32139    32139           
  Misses       2001     2001           

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[facebook-github-bot]

@saitcakmak has imported this pull request. If you are a Meta employee, you can view this diff on Phabricator.

[danielcohenlive]

Looks like the test plan failed.

[saitcakmak]

@danielcohenlive Yeah, it triggered a branch projection rule despite the "build-tutorials-with-pinned-botorch" workflow that the rule requires passing in the same run. I'll update once we decide on how to get around that.

[saitcakmak]

abandoned