Move connector into internal package, in preparation for profiles

[dmathieu]

Description

This splits the connector package, so the APIs are in an internal package, and redefined publicly for logs/metrics/traces.
In preparation for adding profiles to the package.

Link to tracking issue

See #10375

cc @mx-psi

[codecov]

Codecov Report

Attention: Patch coverage is 99.57447% with 1 line in your changes missing coverage. Please review.

Project coverage is 92.27%. Comparing base (6fcebdb) to head (aafe5b4).
Report is 1 commits behind head on main.

Files	Patch %	Lines
connector/internal/factory.go	99.11%	1 Missing ⚠️

Additional details and impacted files

@@           Coverage Diff           @@
##             main   #10524   +/-   ##
=======================================
  Coverage   92.26%   92.27%           
=======================================
  Files         395      397    +2     
  Lines       18703    18723   +20     
=======================================
+ Hits        17257    17277   +20     
  Misses       1086     1086           
  Partials      360      360           

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[dmathieu]

This technically doesn't change any public API. So I suppose it doesn't need a changelog entry.

[evan-bradley]

Tests all pass and the organization looks good to me.