ci: Ensure assignees can be set for generated PRs (#62418)

Now, this is one of these beautiful cases where GitHubs API ist just so
pleasant to work with: Because PRs are treated as issues, assigning an
assignee to a PR suddenly requires issue write permissions, despite the
issue in question being a PR. Not having that permission resulted in
some missing assignees on zed zippy bumps and failures of the workflows
as seen in
https://github.com/zed-industries/zed/actions/runs/31339736929/job/93311493258.

In comparison, labelling PRs requires PR write permissions as seen in
https://github.com/zed-industries/zed/pull/61525 🤡

Beautiful API and a pleasure to work with, 10/10 would recommend. 

Release Notes:

- N/A