refactor(playground): adopt the sync controllers

[marcus-pousette]

What this does

Replaces the playground's bespoke outbound upload loop and inbound subscription bookkeeping with the controllers from #137 and #138.

• Queue committed local operations through the outbound controller.
• Register the remote WebSocket as the exact-operation upload target.
• Keep local mesh transports attached directly to SyncPeer.
• Express desired child/all subscriptions declaratively through the inbound controller.
• Route manual, scoped, and automatic pulls through the all-target completion contract.
• Handle aggregate failures per peer.
• Keep capability-revoked peers connected while removing genuinely dead transports.

Why

The playground previously duplicated upload queueing, timeout handling, peer selection, and per-peer subscription lifecycle beside SyncPeer. After this change, the UI owns only application policy and connection state; retry preservation, target replacement, subscriptions, cancellation, and aggregate completion live in the tested controllers.

Debloat and fast paths

This is a net deletion: 9 files, +358/-520 (net -162).

• Exact committed operations push directly; normal edits do not rescan the full log.
• Local-tab transports do not enter the remote upload loop.
• Unchanged transports and subscriptions are reused.
• Error classification is dependency-free and runs only after a failure.
• No polling loop or new transport abstraction is added.

Verification

• playground TypeScript passes after the fix(auth): bind outbound ops to validated capability snapshots #191 restack
• sync protocol: 58/58
• @treecrdt/sync: 32/32
• git diff --check passes
• GitHub CI rebuilds the generated wa-sqlite browser asset required by the Vite/browser jobs

This UI-only layer is stacked on #138 through the stack/inbound-sync-controller mirror.