feat: Add support for private registries endpoints

[acouvreur]

Adds support for private registries endpoints.

See https://docs.github.com/rest/private-registries for more details.

script/generate.sh, script/fmt.sh and script/lint.sh have been run without issue.

Closes#3784

[gmlewis]

I think the linter is going to catch some things, but here is some early feedback.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 91.54%. Comparing base (036aeb4) to head (8dea44d).
⚠️ Report is 2 commits behind head on master.

Additional details and impacted files

@@ Coverage Diff @@## master #3785 +/- ##
==========================================
+ Coverage 91.50% 91.54% +0.04% 
==========================================
Files 190 191 +1 Lines 17007 17088 +81 ==========================================
+ Hits 15562 15643 +81 
Misses 1257 1257 Partials 188 188 

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[gmlewis]

Thank you, @acouvreur!
LGTM.
Awaiting second LGTM+Approval from any other contributor to this repo before merging.

cc: @stevehipwell - @alexandear - @zyfy29

[gmlewis]

Thank you, @alexandear!
Merging.