docs: document AI providers seeding mechanism & support for new types (#25855)

Adds a new **Provider Configuration** reference page (`providers.md`) covering:

- The migration from environment-variable-based provider config to database-backed management introduced in v2.34, including the one-time seeding behavior and deprecation of `CODER_AI_GATEWAY_PROVIDER_<N>_*` and related flags
- All supported provider types (`openai`, `anthropic`, `bedrock`, `copilot`, `azure`, `google`, `openrouter`, `vercel`, `openai-compat`) with setup notes for each
- Provider lifecycle statuses (`enabled`, `disabled`, `error`) and their effect on request handling
- Reload behavior and how configuration changes apply without restarting `coderd`
- Bring Your Own Key (BYOK) and failure mode reference table

Updates **Setup** (`setup.md`) to replace the environment-variable-based provider configuration instructions with dashboard-driven steps (Add provider form, provider list, edit/disable flow), referencing the new `providers.md` page for deeper detail. Screenshots of the provider list, add, and edit forms are included.

Adds a **Provider metrics** section to **Monitoring** (`monitoring.md`) documenting the `coder_aibridged_*` and `coder_aibridgeproxyd_*` Prometheus metrics for provider status and reload timestamps, along with two suggested PromQL alert queries.

docs/manifest.json

@@ -1252,6 +1252,12 @@
 										}
 									]
 								},
+								{
+									"title": "Provider Configuration",
+									"description": "How AI Gateway stores, seeds, and reloads provider configuration",
+									"path": "./ai-coder/ai-gateway/providers.md",
+									"state": ["ai governance add-on"]
+								},
 								{
 									"title": "Auditing AI Sessions",
 									"description": "How to audit AI sessions",