Move processor into an internal package, in preparation for profiles

[dmathieu]

Description

This splits the processor 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 98.90110% with 1 line in your changes missing coverage. Please review.

Project coverage is 92.28%. Comparing base (05cdcf4) to head (0bc3fd5).
Report is 1 commits behind head on main.

Files	Patch %	Lines
processor/internal/factory.go	97.77%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main   #10526      +/-   ##
==========================================
- Coverage   92.28%   92.28%   -0.01%     
==========================================
  Files         397      399       +2     
  Lines       18723    18731       +8     
==========================================
+ Hits        17279    17285       +6     
- Misses       1085     1086       +1     
- Partials      359      360       +1     

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