Implement Peft active-table reporting in this game.

First check whether this feature is already implemented. Verify existing behavior against the requirements and acceptance cases below, using tests and available runtime checks. If it already satisfies them, leave working code unchanged and report the verification evidence. If it is partial or broken, implement only the missing behavior or fixes; do not duplicate integrations, callbacks, or state. Report anything you could not verify instead of assuming success.

Prerequisite: Peft room links and direct joining must already work. Inspect the current networking lifecycle and preserve gameplay, protocol, and existing integrations. Implement only this feature. Report missing prerequisites explicitly.

Peft supplies window.PEFT alongside window.PEFT_LAUNCH:
- await window.PEFT.hostRoom(actualRoomCode, optionalPlayerCount)
- await window.PEFT.joinedRoom(actualRoomCode)
- await window.PEFT.closeRoom(actualRoomCode)

- Wire these to confirmed networking callbacks, NOT simply button clicks. Only an actual host calls hostRoom after the real room exists.
- Use actual network-issued room codes, 1-64 ASCII letters/digits/underscores/hyphens. Do not advertise placeholders or PREVIEW just because a page opened.
- hostRoom advertises the room on Peft's signed-in homepage and returns its canonical, version-pinned invite. The wrapper updates the browser address without reloading gameplay.
- joinedRoom updates the address and returns an invite but creates no duplicate listing and takes no ownership. It stops any hosting advertisement from this page.
- closeRoom removes this host page's listing. Call it when hosting ends, the room closes, or the networking layer knows the host connection has been lost.
- The wrapper renews hosting every thirty seconds while open; listings expire after two minutes without updates. A listing is not proof the network will accept a join.
- Handle promise rejections visibly. Listen for peft-room-error events for later heartbeat failures, report failures, and explicitly report hosting again after connectivity returns.
- Call hostRoom again when the real room or optional player count changes, avoiding rapid repeated reports. One host page advertises one table; another code replaces its previous listing.
- Report host migration only after networking confirms takeover. Overlapping listings may be rejected until the original closes/expires.
- Guard every call with if (window.PEFT) for standalone launch and the networkless screenshot renderer. Do not fake success when the bridge is absent.
- Joining from Peft's homepage must read PEFT_LAUNCH.room and join that exact room. Reporting alone does not implement joining.
- Do not access parent DOM, expose private runtime URLs or credentials, or change the sandbox.

Add tests around confirmed hosting/joining/closure, player-count updates, bridge rejection, peft-room-error, recovery, and absent bridge. Exercise a real host appearing on Peft, a participant joining without duplicate listings, and disappearance after closure or expiration. Ensure repeated room-links integration does not install duplicate callbacks or reports.

Report changed files, test commands/results, lifecycle wiring, external requirements, and actual limitations. Do not claim live Peft acceptance unless exercised.