enhance(websocket): improve client synchronization (#38847)

Keep notification counts and stopwatches in sync when tabs open or
reconnect, closing the gap behind [this
flake](https://github.com/go-gitea/gitea/actions/runs/31312525323/job/93242429394).

1. Send current notification counts and stopwatch state on each
WebSocket connection, replacing the separate state fetches tabs made on
every connect.
2. Tabs joining an already open connection fetch current state once,
since its snapshot went out before they attached.
3. Send events queued during the handshake before the snapshot, so older
events can't roll it back.
4. Wait for the Redis SUBSCRIBE acknowledgement, so the snapshot read
after subscribing can't miss an event.

services/websocket/websocket_test.go

@@ -0,0 +1,19 @@
+// Copyright 2026 The Gitea Authors. All rights reserved.
+// SPDX-License-Identifier: MIT
+
+package websocket
+
+import (
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+)
+
+func TestEventForSessionTargetsAndKeepsEmptyData(t *testing.T) {
+	targeted := makeEventMessage("targeted-event", "sess-A", nil)
+	assert.JSONEq(t, `{"eventType":"targeted-event"}`, string(EventForSession(targeted, "sess-A")))
+	assert.Nil(t, EventForSession(targeted, "sess-B"))
+
+	broadcast := makeEventMessage("list-event", "", []int{})
+	assert.JSONEq(t, `{"eventType":"list-event","eventData":[]}`, string(EventForSession(broadcast, "sess-A")))
+}