fix: 800ms delay before first inbound notification

Race observed on first turn: ClaudePlugin emits
notifications/claude/channel before Claude Code finishes registering
the channel handler internally. Claude logs
"MCP server synthesis: Channel notifications registered" ~25ms AFTER
hello_ack arrives. Notifications that arrive earlier are silently
dropped — observed empty session, no turn, curl hangs until timeout.

Fix: on first `inbound` frame after WS hello, wait 800ms before
emitting the MCP notification. Subsequent inbounds skip the wait.

End-to-end verified twice on laptop. Cold-start ~10s, hot path 2-3s.

server.ts

@@ -98,6 +98,7 @@ mcp.setRequestHandler(CallToolRequestSchema, async req => {
 let ws: WebSocket | null = null
 let backoff = 1000
 const outbox: unknown[] = []
+let firstInboundDelivered = false
 
 function bridgeSend(frame: unknown): void {
   if (ws && ws.readyState === WebSocket.OPEN) {
@@ -147,6 +148,16 @@ async function handleBridge(frame: any): Promise<void> {
       log(`hello_ack received`)
       return
     case 'inbound':
+      // Race guard: Claude Code's internal "Channel notifications registered"
+      // log line appears ~25ms AFTER we send hello_ack — if we push the
+      // notification before then, claude silently drops it. Buffer the
+      // first inbound briefly to dodge this. Subsequent inbounds don't
+      // need the wait (channel is registered for the lifetime of the
+      // session).
+      if (!firstInboundDelivered) {
+        await new Promise(r => setTimeout(r, 800))
+        firstInboundDelivered = true
+      }
       await mcp.notification({
         method: 'notifications/claude/channel',
         params: {