settings ui: Adjust project dropdown design a bit (#40260)

Makes the dropdown trigger button styling consistent with the other
buttons and allows to add a tooltip in the trigger through the popover's
`trigger_with_tooltip` method.

Release Notes:

- N/A
3e2680d650Danilo Leal committed on 10/15/2025, 4:55:57 PM· committed by GitHubparent35595fe
2 files changedLine totals unavailable