test(coderd): centralize chat test harness and stabilize flakes (#25171)

Chat tests previously constructed a real `openai` provider with a fake
API key and no `BaseURL`, so background title generation hit
`api.openai.com` and timed out under `-race`. The same root cause
produced several distinct flakes: title regeneration races with
synchronous `UpdateChat`/`ProposeChatTitle`, and pagination races
against `updated_at` bumps from real-network processing.

This moves the fake OpenAI-compatible provider and the chat-settle wait
into first-class `coderdtest` capabilities.
`coderd.Options.ChatProviderAPIKeys` is the new seam tests use to
redirect chat traffic to a local `httptest.Server`.
`coderdtest.WaitForChatSettled` replaces per-test waiters and drains
tracked chat-daemon work after the chat row leaves `pending`/`running`.
The `newChatClient*` constructors funnel through one options builder
that installs the fake provider before the coderd test server so cleanup
ordering is deterministic.

Closes https://github.com/coder/internal/issues/1528 & Closes ENG-2659
Closes https://github.com/coder/internal/issues/1480 & Closes CODAGT-359
Closes https://github.com/coder/internal/issues/1507 & Closes CODAGT-368
Relates to https://github.com/coder/internal/issues/1397 & Relates to
CODAGT-374

coderd/x/chatd/export_test.go

@@ -10,14 +10,6 @@ import (
 	"github.com/coder/coder/v2/codersdk"
 )
 
-// WaitUntilIdleForTest waits for background chat work tracked by the server to
-// finish without shutting the server down. Tests use this to assert final
-// database state only after asynchronous chat processing has completed.
-// Close waits for the same tracked work, but also stops the server.
-func WaitUntilIdleForTest(server *Server) {
-	server.drainInflight()
-}
-
 // FinishActiveChatForTest exposes the unexported cleanup TX so tests
 // can drive the post-run state machine deterministically. Returns the
 // resulting chat, the promoted message (if any), the synthetic

coderd/x/chatd/testhooks.go

@@ -0,0 +1,9 @@
+package chatd
+
+// WaitUntilIdleForTest waits for background chat work tracked by the server to
+// finish without shutting the server down. Tests use this to assert final
+// database state only after asynchronous chat processing has completed.
+// Close waits for the same tracked work, but also stops the server.
+func WaitUntilIdleForTest(server *Server) {
+	server.drainInflight()
+}