The More menu passed the tab's raw `profileId` to the clear actions. A tab
created before profiles existed has none, and the IPC layer reads an absent
profile as "every profile" — so a menu labelled "Clear cookies (Default)" wiped
every partition. The view now resolves the default the same way it resolves the
name it displays, and the prop is required so the gap cannot come back.

Clearing also only touched sessions already in the in-memory map. Deriving the
partition string does not create the session, so clearing a profile with no tab
open this run reported success and deleted nothing; the handler now loads the
session first.

`resolveBrowserProfiles` additionally drops repeated ids, which map to one
partition and would otherwise show as two isolated identities sharing every
cookie, and reports a custom `incognito` profile as persistent, since
persistence is keyed off the built-in id alone.

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