[popover] Popover loses focus when using `Activity`

[OliverJAsh]

Bug report

Current behavior

1. Open the popover
2. Click the "show" button
3. Press tab

The buttons outside the popover has focus. The popover remains open.

Expected behavior

The popover should retain focus.

Reproducible example

https://stackblitz.com/edit/eldph4db?file=src%2FApp.tsx

Base UI version

1.0.0-beta.6

Which browser are you using?

Chrome

Which OS are you using?

Mac OS

Which assistive tech are you using (if applicable)?

Voiceover/JAWS etc.

Additional context

The issue does not occur when not using Activity.

If it helps, here is a real world example:

Screen.Recording.2025-11-21.at.09.08.20.2.mov