fix(api): preserve base URL paths in Twirp requests

[Kayvan-Zahiri]

When LiveKitAPI is given a URL such as https://example.com/proxy/livekit, API requests currently go to /twirp/... and drop /proxy/livekit. A proxy that routes the API under that path therefore returns 404. The request loop builds URLs from the origin, which intentionally excludes the path.

Keep the normalized base path separately and include it when constructing each Twirp request, including retries. This also removes the extra slash inserted while reconstructing self.host.

Added local HTTP-server regressions covering HTTP and WebSocket-style URLs, empty and nested base paths, trailing slashes, and failover with default/custom Twirp prefixes. The failover tests also verify the request body and idempotency key stay the same across attempts.

Validation:

• The prefixed-route cases reproduce a 404 before the fix; unprefixed routes pass.
• pytest tests/api against the official LiveKit mock server bound to localhost: 46 passed (Python 3.12).
• Ruff lint/format checks for the new tests and git diff --check: pass.

[CLAassistant]

All committers have signed the CLA.