Adds the create/rename/remove list and a picker for which profile new tabs
open under, including tabs an agent opens.

Built-ins render without controls: they are synthesized rather than stored, so
there is nothing to rename, and removing them would strand every tab already
opened under them. A test covers the matching invariant — a hand-edited
settings file cannot shadow Default or Incognito with a stored entry.

Removing a profile clears its partition's cookies and cache, otherwise its
logins would sit on disk with nothing in the UI pointing at them, and reassigns
the default if it pointed at the removed profile.

Names commit on blur via DraftInput rather than per keystroke, matching the
dimension fields.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>