fix(coderd/x/chatd): stabilize advisor stream test (#25781)

`TestAdvisorHappyPath_RootChat` could subscribe after the active test
server had already processed the chat and published transient advisor
deltas, leaving the live delta collector empty.

Use a passive chatd test server until the live subscriber and collector
are registered, then start processing and wait for the expected advisor
deltas before canceling the stream.

Closes coder/internal#1548

Generated by Coder Agents.

<details>
<summary>Implementation notes</summary>

The failing assertion covered stream-only advisor `ResultDelta` events.
`CreateChat` signals the processor, so an already-started server can
publish those deltas before `Subscribe` registers its local stream
subscriber. The test now creates the chat on a passive server,
subscribes, starts the collector, then calls `Start()`.

</details>

coderd/x/chatd/chatd_test.go

@@ -26,6 +26,7 @@ import (
 	mcpserver "github.com/mark3labs/mcp-go/server"
 	"github.com/prometheus/client_golang/prometheus"
 	"github.com/sqlc-dev/pqtype"
+	"github.com/stretchr/testify/assert"
 	"github.com/stretchr/testify/require"
 	"go.uber.org/mock/gomock"
 	"golang.org/x/xerrors"
@@ -9914,7 +9915,7 @@ func TestAdvisorHappyPath_RootChat(t *testing.T) {
 		MaxUsesPerRun:   3,
 		MaxOutputTokens: 16384,
 	})
-	server := newActiveTestServer(t, db, ps)
+	server := newTestServer(t, db, ps, uuid.New())
 
 	chat, err := server.CreateChat(ctx, chatd.CreateOptions{
 		OrganizationID: org.ID,
@@ -9927,13 +9928,7 @@ func TestAdvisorHappyPath_RootChat(t *testing.T) {
 	})
 	require.NoError(t, err)
 
-	// Subscribe before the worker commits any durable messages so we
-	// observe the advisor tool-result deltas live. Buffered parts are
-	// claimed by their committed durable message ID at publishMessage
-	// time and dropped from snapshots of late-connecting subscribers, so
-	// a post-completion Subscribe() would no longer see streaming
-	// deltas. Collecting events from the live channel covers the
-	// streaming UX contract this test exists to verify.
+	// Advisor deltas are transient; a late subscriber misses them.
 	_, liveEvents, cancelLive, ok := server.Subscribe(ctx, chat.ID, nil, 0)
 	require.True(t, ok)
 	var (
@@ -9969,6 +9964,8 @@ func TestAdvisorHappyPath_RootChat(t *testing.T) {
 		}
 	}()
 
+	server.Start()
+
 	require.Eventually(t, func() bool {
 		got, getErr := db.GetChatByID(ctx, chat.ID)
 		if getErr != nil {
@@ -10023,17 +10020,15 @@ func TestAdvisorHappyPath_RootChat(t *testing.T) {
 	require.True(t, parentSawAdvisorResult,
 		"parent must see the advisor reply in its continuation call")
 
-	// Stop the live collector and assert it captured the streaming
-	// advisor deltas during processing. Late subscribers no longer
-	// see committed parts because publishMessage claims them out of
-	// new snapshots, so the assertion must use the live collector.
+	require.EventuallyWithT(t, func(c *assert.CollectT) {
+		livePartsMu.Lock()
+		defer livePartsMu.Unlock()
+		assert.Equal(c, advisorDeltas, liveAdvisorDeltas,
+			"advisor nested text deltas must stream into the parent tool card")
+	}, testutil.WaitLong, testutil.IntervalFast)
+
 	cancelLive()
 	<-liveCollectorDone
-	livePartsMu.Lock()
-	collectedAdvisorDeltas := append([]string(nil), liveAdvisorDeltas...)
-	livePartsMu.Unlock()
-	require.Equal(t, advisorDeltas, collectedAdvisorDeltas,
-		"advisor nested text deltas must stream into the parent tool card")
 
 	persisted, err := db.GetChatMessagesByChatID(ctx, database.GetChatMessagesByChatIDParams{
 		ChatID:  chat.ID,