fix(chrome): debounce sync-to-chrome export and set the exported profile's display name

[ankitranjan7]

Summary

Two follow-up fixes found while manually testing the just-shipped v0.8.3 Chrome-profile-export feature:

1. Export was gated on the browser being fully idle-closed, which in practice almost never happens

• scheduleProfileIdle's idle timer never even gets set while any tab from the profile is still open (hasVisiblePages guard) — and browser run doesn't close its own resulting tab. Confirmed live: a profile sat "connected" for 4+ minutes with a tab open and only exported once its session was explicitly closed, which nobody would know to do.
• Fix: export is decoupled from closing the browser entirely. A new, independent per-profile debounce timer (3s, reset on every command, not gated on open tabs) triggers the export — copy cookies, register if new — without touching the browser or any open page. The existing close-triggered export remains as a harmless, idempotent backstop.

2. Exported profiles show up in Chrome as "Person 2", "Person 3", etc. instead of their real webcmd alias

• Chrome auto-registers a newly exported profile-directory but assigns it a generic name, since nothing goes through Chrome's own profile-creation UI.
• Fix: after the invisible registration-trigger process has actually exited (waiting briefly post-signal, to avoid Chrome's own shutdown flush clobbering our edit), write the profile's Local State display name to match the webcmd alias exactly (e.g. test1 shows as test1). Best-effort and silent on failure — purely cosmetic, never blocks the export. Documented limitation: if native Chrome was already running (registration got absorbed into the existing process rather than spawning a separate one), there's nothing safe to wait on, and the name write may later get overwritten by Chrome's own state flush.

Test plan

• Full suite: 206 test files, typecheck clean (confirmed under reduced worker concurrency — full-parallelism hits the same pre-existing runner.test.ts browser-context flakiness under high system load documented in prior PRs; all three files this PR touches pass 106/106 in isolation)
• New tests cover: export firing ~3s after a command with the tab still open, a burst of rapid commands collapsing into one export, the debounced export never closing the browser/page, no debounce for non-sync-to-chrome profiles, display name being set after a spawned registration process is confirmed killed, the best-effort case when Chrome was already running, and display name never being set when registration times out

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[github-actions]

🟠 Maintainer review suggested — low confidence

The automated review could not reach a fully supported conclusion.

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This review is advisory and does not block merging.