[client, consumer] Move client features to consumerconnection

[TylerHelmuth]

Description

This PR moves client features to consumerconnection. This attempts to remove ambiguity from the name client and continues to centralizes consumer as the location for features that pass data between components.

Link to tracking issue

Related to #9818

Testing

Duplicated the unit tests

Documentation

Updated the package comments and added deprecated warnings to the old client package.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 91.78%. Comparing base (fcdfdaa) to head (bc7f2f5).
Report is 35 commits behind head on main.

❗ Current head bc7f2f5 differs from pull request most recent head ffdf862. Consider uploading reports for the commit ffdf862 to get more accurate results

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #9996      +/-   ##
==========================================
+ Coverage   91.77%   91.78%   +0.01%     
==========================================
  Files         359      361       +2     
  Lines       16633    16657      +24     
==========================================
+ Hits        15265    15289      +24     
  Misses       1041     1041              
  Partials      327      327              

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

[bogdandrutu]

consumerconnection go likes shorter names, conn is a good replacement for connection.

Not sure if is not cleaner to have consumer.ConnInfo instead? OR consumerinfo.Conn and consumerinfo.AuthData?

[TylerHelmuth]

Updated to consumerconn for now. That gives us consumerconn.Info and consumerconn.AuthData which I like since sharing connection data is the overall theme of the package and Info and AuthData are pieces of connection data the package supports sharing.