branch_picker: Add design improvements (#60925)

This PR adds a series of design improvements to the branch picker,
including:

- Consistent icon used for filter actions
- A keybinding/action to trigger the filter menu with the keyboard
- Filter menu positioning depending on the picker's editor position
- Error display that displays the full label without truncation/tooltip,
and is placed accordingly also depending on the picker's editor position
- List subheader in the search list depending on filtered option

Here's a quick video:


https://github.com/user-attachments/assets/70922daf-fc9f-4d94-bed8-c84d3ea73534

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Release Notes:

- N/A
a04a47e1efDanilo Leal committed on 7/14/2026, 11:11:55 AM· committed by GitHubparent5e982c6
5 files changedLine totals unavailable