feat: drop dependency on gh

[JoshuaKGoldberg]

PR Checklist

• Addresses an existing open issue: fixes 🚀 Feature: Drop end-user dependency on gh #667
• That issue was marked as status: accepting prs
• Steps in CONTRIBUTING.md were taken

Overview

Replaces the end-user dependency on gh (the GitHub CLI) with more manual Octokit calls. It's a bit less convenient this way but is more type-safe and means users don't need to have some random GitHub utility installed to use the template.

Update December 7th: this works but I don't like how the user has to either have gh logged in or use a process.env.GH_TOKEN... I'd like to find the time to look into alternatives to log the user in.

[codecov]

Codecov Report

Attention: 3 lines in your changes are missing coverage. Please review.

Comparison is base (b3c7970) 94.18% compared to head (7fb6308) 94.21%.
Report is 1 commits behind head on main.

Files	Patch %	Lines
src/create/createWithOptions.ts	0.00%	1 Missing ⚠️
src/initialize/initializeWithOptions.ts	0.00%	1 Missing ⚠️
src/steps/initializeGitHubRepository/index.ts	0.00%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #1000      +/-   ##
==========================================
+ Coverage   94.18%   94.21%   +0.03%     
==========================================
  Files          97       97              
  Lines        5620     5667      +47     
  Branches      457      462       +5     
==========================================
+ Hits         5293     5339      +46     
- Misses        326      327       +1     
  Partials        1        1              

Flag	Coverage Δ
create	69.61% <9.52%> (-0.64%)	⬇️
initialize	41.67% <14.28%> (-0.49%)	⬇️
migrate	68.95% <9.52%> (-0.63%)	⬇️
unit	72.38% <96.42%> (+0.23%)	⬆️

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[JoshuaKGoldberg]

For retrieving a user auth token, JoshuaKGoldberg/prune-github-notifications#167 also tracks creating a standalone package.