Add more E2E tests for Responses api and Conversations api

[srampal]

Reminder to add these as a follow up to #2133 once that PR is merged

[srampal]

The vllm simulator also needs to add support for responses api (and conversations api) first. There are open issues for that already. llm-d/llm-d-inference-sim#260
Once that is done the E2E tests for these apis in this repo can be further expanded via this issue.