refactor(git): prepare support for commit signing with other key formats

[sisp]

Changes

I've refactored the implementation for commit signing as a preparatory step for supporting other key formats like SSH.

Context

I submitted a PR (#29550) that adds support for SSH-based commit signing which currently includes a refactoring to support multiple key formats. During review, it was suggested to do the refactoring in a separate PR (#29550 (comment)).

Once this PR has been merged, I'll update #29550 accordingly.

Documentation (please check one with an [x])

• I have updated the documentation, or
• No documentation update is required

How I've tested my work (please select one)

I have verified these changes via:

• Code inspection only, or
• Newly added/modified unit tests, or
• No unit tests but ran on a real repository, or
• Both unit tests + ran on a real repository

[renovate-release]

🎉 This PR is included in version 37.421.1 🎉

The release is available on:

• GitHub release
• npm package (@latest dist-tag)
• 37.421.1

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