metrics/log_encoder: Log metrics in JSON format too

[Turbo87]

This format can be parsed by Datadog to recreate some of our remaining Grafana graphs in that system too:

[codecov]

Codecov Report

Attention: Patch coverage is 92.85714% with 1 line in your changes missing coverage. Please review.

Project coverage is 88.92%. Comparing base (6347fbb) to head (61bb08a).
Report is 8 commits behind head on main.

Files with missing lines	Patch %	Lines
src/metrics/log_encoder.rs	92.85%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #9711      +/-   ##
==========================================
- Coverage   88.93%   88.92%   -0.01%     
==========================================
  Files         288      288              
  Lines       29630    29645      +15     
==========================================
+ Hits        26350    26363      +13     
- Misses       3280     3282       +2     

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