Backport "[PROF-9472] Add recorder_stats and profile_stats to internal metadata" to 1.x-stable

[ivoanjo]

What does this PR do?

This PR backports #3583 to the 1.x-stable branch. See original PR for more details.

Motivation:

This tweak also makes sense to apply on the 1.x-stable series.

Additional Notes:

I cherry-picked the upstream commits with no other changes.

How to test the change?

See original PR for details.

[codecov-commenter]

Codecov Report

Attention: Patch coverage is 97.53086% with 2 lines in your changes are missing coverage. Please review.

Project coverage is 98.24%. Comparing base (09ba2b0) to head (d35e22c).
Report is 1 commits behind head on 1.x-stable.

Files	Patch %	Lines
spec/datadog/profiling/stack_recorder_spec.rb	96.82%	2 Missing ⚠️

Additional details and impacted files

@@             Coverage Diff             @@
##           1.x-stable    #3620   +/-   ##
===========================================
  Coverage       98.24%   98.24%           
===========================================
  Files            1255     1255           
  Lines           74569    74638   +69     
  Branches         3540     3544    +4     
===========================================
+ Hits            73262    73331   +69     
  Misses           1307     1307           

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