ci: Use `zed-zippy` identity for `bump_patch_version.yml` (#46099)

This PR updates the `bump_patch_version.yml` to also be generated by
`cargo xtask workflows` and updates this to use the `zed-zippy` identity
instead of the `ConradIrwin` identity.

Release Notes:

- N/A
e07a304c32Finn Evers committed on 1/5/2026, 7:53:16 PM· committed by GitHubparent72c7a31
4 files changedLine totals unavailable