feat: add /api/v2/ai-gateway API route aliases (#26475)

## Description

Registers `/api/v2/ai-gateway/*` as the new API path for AI Gateway, replacing `/api/v2/aibridge/*`. Both prefixes share the same route builder (`aiBridgeRoutes`) backed by a single in-memory handler, so existing `/aibridge` endpoints continue to work. New endpoints must be registered on the enterprise API handler under `/api/v2/ai-gateway` only.

Swagger annotations now point to `/api/v2/ai-gateway` paths with a backward-compatibility note referencing `/aibridge`. The legacy `/aibridge` routes are skipped in the swagger documentation test.

## Changes

- Store one raw handler (`aiGatewayHandler`) instead of two prefix-stripped handlers
- Register `/ai-gateway` and `/ai-gateway/proxy` route aliases alongside legacy `/aibridge` routes
- Move `/aibridge/keys` to `/ai-gateway/keys`
- Update in-process transport to use `/api/v2/ai-gateway` prefix
- Update SDK client URLs and proxy forwarding URL
- Swap `@Router` and `@Tags` annotations from `aibridge`/`AI Bridge` to `ai-gateway`/`AI Gateway`
- Rename user-facing error messages from "AI Bridge" to "AI Gateway"
- Define consts for route prefixes (`AIGatewayRootPath`, `AIBridgeRootPath`)
- Update tests and comments to use new paths

Note: the following will be addressed in follow-up PRs:
- Frontend API URLs
- Frontend routes and redirects
- Dogfood main.tf updates
- Hand-written documentation URL updates
- aibridge internal comments and nits
- Scale tests path updates

Refs https://linear.app/coder/issue/AIGOV-230

> Generated with the assistance of Coder Agents (@ssncferreira)

docs/manifest.json

@@ -1521,8 +1521,8 @@
 							"path": "./reference/api/general.md"
 						},
 						{
-							"title": "AI Bridge",
-							"path": "./reference/api/aibridge.md"
+							"title": "AI Gateway",
+							"path": "./reference/api/aigateway.md"
 						},
 						{
 							"title": "AI Providers",