fix: do not attempt to create pull request when no changes detected

[rrey]

Proposing a fix for #2551 where the root cause is mainly identified in the issue.

Disclamer:

• I used Claude Code to write this change but took time to look at the propose change and requested the additional test coverage.
• I also checked that the issue was actually fixing the issue on one of the repos where we faced the issue by first reproducing the issue locally with an official release-please release and with the locally built version including my change

Checks:

• Make sure to open an issue as a bug/issue before writing your code! That way we can discuss the change, evaluate designs, and agree on the general idea
• Ensure the tests and linter pass
• Code coverage does not decrease
• Appropriate docs were updated (not required)

Fixes #2551