Simplify `_process_changelog` in `generator/cli.py`

[parthea]

See feedback from @ohmayr in https://github.com/googleapis/google-cloud-python/pull/14353#discussion_r2331393020 referring to the code block below:

I think we can refactor these text replacements into their own functions. This will make unit testing easier and cleaner where we can test each of these separately and will probably clean up this function as well. This is not a blocker so feel free to skip if you disagree.

https://github.com/googleapis/google-cloud-python/blob/6405a6ee3e08ab2771f226ee8a5ea1189628170a/.generator/cli.py#L609-L673

We can extract code into help functions to improve readability and testability.