chore: use GITHUB_TOKEN to create sync PRs

[brian-smith-tcril]

Description

We were using the same token to create and approve the sync PRs, leading to

Error: Unprocessable Entity: "Can not approve your own pull request". This typically happens when you try to approve the pull request with the same user account that created the pull request. Try using the built-in `${{ secrets.GITHUB_TOKEN }}` token, or if you're using a personal access token, use one that belongs to a dedicated bot account.

This isn't an issue for https://github.com/openedx/paragon/blob/release-23.x/.github/workflows/analyze-dependents.yml, which uses https://github.com/peter-evans/create-pull-request as opposed to https://github.com/TreTuna/sync-branches

https://github.com/peter-evans/create-pull-request has token as optional, and has the default documented as GITHUB_TOKEN

This PR updates the sync workflow to create PRs using secrets.GITHUB_TOKEN, while keeping the approval token the same.

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[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 93.87%. Comparing base (a633633) to head (36f2f59).
Report is 1 commits behind head on release-23.x.

Additional details and impacted files

@@              Coverage Diff              @@
##           release-23.x    #3360   +/-   ##
=============================================
  Coverage         93.87%   93.87%           
=============================================
  Files               232      232           
  Lines              3937     3937           
  Branches            933      933           
=============================================
  Hits               3696     3696           
  Misses              237      237           
  Partials              4        4           

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