[Cosmos] custom transport prep work

Follow-up to https://github.com/Azure/azure-sdk-for-python/pull/37419, which I had previously closed.

As part of the HTTP/2 readiness for the SDK, in order to handle custom transports, there was a couple things we had to do:

make sure we can deal with response.content, which will be the new way to process the response data
remove areas where we are manually setting values into response headers, since the possibility exists of now receiving immutable response headers due to HTTP/2's performance optimizations

With these changes we ensure our SDK is HTTP/2 ready.

Also took the opportunity to update our logs to reflect what it should actually have looked like for the logger setup to work as expected when used on a per-request basis - just having the logger named azure would make it a parent that would log all of the requests due to the policy's call to super.__init__().

Azure / azure-sdk-for-python

[Cosmos] custom transport prep work #38640