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/ai-coder/ai-gateway/monitoring.md

@@ -131,7 +131,7 @@ Available query filters:
 - `started_after` - Filter sessions after a timestamp
 - `started_before` - Filter sessions before a timestamp
 
-See the [API documentation](../../reference/api/aibridge.md) for full details.
+See the [API documentation](../../reference/api/aigateway.md) for full details.
 
 ## Data Retention