fix(router): unify route_request to async with optional request_json

[nejch]

proxy_multipart_request calls router.route_request without the request_json argument, which causes a TypeError when the router is a SessionRouter since those require request_json as a positional parameter. This was introduced by f1265a0 which added request_json as a required parameter to SessionRouter.route_request but didn't update proxy_multipart_request.

The affects /v1/audio/transcriptions and /v1/images/edits endpoints when using session-based routers.

This PR makes request_json an optional parameter and makes all routers' route_request async.

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[gemini-code-assist]

Code Review

This pull request updates routing_logic.py to handle request_json as an optional parameter in the RoutingInterface and RoundRobinRouter implementations, while also improving null safety in extract_session_id. However, the review highlights that the changes are incomplete as several other router subclasses still require request_json as a mandatory argument, which will cause TypeError during execution. Furthermore, there is a potential issue where synchronous calls to asynchronous router methods will return coroutines instead of the expected URL strings.

[ruizhang0101]

@nejch Hi, Could you fix the CI issue when you have time?