Code Review: improve base dropdown UX

Here's what it is today:

<img width="3924" height="2462" alt="Image" src="https://github.com/user-attachments/assets/05c5689f-51a2-45a0-b47d-50951c33e949" />

Instead, we could show some of those default options, but instead of HEAD* we could show recent commit hashes and their messages. The search could also apply to messages to make it more humane.

The styling could use some work too