perf(coderd/x/chatd): add process-wide config cache for hot DB queries (#23272)

## Summary

Adds a process-wide cache for three hot database queries in `chatd` that
were hitting Postgres on **every chat turn** despite returning
rarely-changing configuration data:

| Query | Before (50k turns) | After | Reduction |
|---|---|---|---|
| `GetEnabledChatProviders` | ~98.6k calls | ~500-1000 | ~99% |
| `GetChatModelConfigByID` | ~49.2k calls | ~500-1000 | ~98% |
| `GetUserChatCustomPrompt` | ~46.7k calls | ~1000-2000 | ~97% |

These were identified via `coder exp scaletest chat` (5000 concurrent
chats × 10 turns) as the dominant source of Postgres load during chat
processing.

## Design

Follows the established **webpush subscription cache pattern**
(`coderd/webpush/webpush.go`):
- `sync.RWMutex` + `tailscale.com/util/singleflight` (generic) +
generation-based stale prevention + TTL
- 10s TTL for provider/model config, 5s TTL for user prompts
- Negative caching for `sql.ErrNoRows` on user prompts (the common case
— most users don't set custom prompts)
- Deep-clones `ChatModelConfig.Options` (`json.RawMessage` = `[]byte`)
on both store and read paths

### Invalidation

Single pubsub channel (`chat:config_change`) with kind discriminator for
cross-replica cache invalidation. Seven publish points in
`coderd/chats.go` cover all admin mutation endpoints
(create/update/delete for providers and model configs, put for user
prompts).

_This PR was generated with mux and was reviewed by a human_

coderd/x/chatd/subagent.go

@@ -72,7 +72,7 @@ func (p *Server) isAnthropicConfigured(ctx context.Context) bool {
 	if p.providerAPIKeys.APIKey("anthropic") != "" {
 		return true
 	}
-	dbProviders, err := p.db.GetEnabledChatProviders(ctx)
+	dbProviders, err := p.configCache.EnabledProviders(ctx)
 	if err != nil {
 		return false
 	}