* fix(route_llm_request.py): move to using common router, even for client-side credentials
ensures fallbacks / cooldown logic still works
* test(test_route_llm_request.py): add unit test for route request
* feat(router.py): generate unique model id when clientside credential passed in
Prevents cooldowns for api key 1 from impacting api key 2
* test(test_router.py): update testing to ensure original litellm params not mutated
* fix(router.py): upsert clientside call into llm router model list
enables cooldown logic to work accurately
* fix: fix linting error
* test(test_router_utils.py): add direct test for new util on router
