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/coderdtest/coderdtest.go

@@ -91,6 +91,7 @@ import (
 	"github.com/coder/coder/v2/coderd/workspaceapps/appurl"
 	"github.com/coder/coder/v2/coderd/workspacestats"
 	"github.com/coder/coder/v2/coderd/wsbuilder"
+	"github.com/coder/coder/v2/coderd/x/chatd/chatprovider"
 	"github.com/coder/coder/v2/codersdk"
 	"github.com/coder/coder/v2/codersdk/agentsdk"
 	"github.com/coder/coder/v2/codersdk/drpcsdk"
@@ -151,6 +152,7 @@ type Options struct {
 	// IncludeProvisionerDaemon when true means to start an in-memory provisionerD
 	IncludeProvisionerDaemon      bool
 	ChatdInstructionLookupTimeout time.Duration
+	ChatProviderAPIKeys           *chatprovider.ProviderAPIKeys
 	ProvisionerDaemonVersion      string
 	ProvisionerDaemonTags         map[string]string
 	MetricsCacheRefreshInterval   time.Duration
@@ -584,6 +586,7 @@ func NewOptions(t testing.TB, options *Options) (func(http.Handler), context.Can
 			// agents are not marked as disconnected during slow tests.
 			AgentInactiveDisconnectTimeout: testutil.WaitShort,
 			ChatdInstructionLookupTimeout:  options.ChatdInstructionLookupTimeout,
+			ChatProviderAPIKeys:            options.ChatProviderAPIKeys,
 			AccessURL:                      accessURL,
 			AppHostname:                    options.AppHostname,
 			AppHostnameRegex:               appHostnameRegex,