connection: use new server module for stream mode

[jkarneges]

Following #47981, this PR updates the stream mode handler to use the refactored server request module. The main goal of this work is to be able to send error responses, however the code to actually send error responses is not included yet in order to keep this PR smaller. Also, the original server request code is commented out instead of removed in order to reduce noise in the diff. This commented-out code will be removed in a later PR.