tracing: Use json-subscriber crate for JSON logging

[Turbo87]

This allows us to flatten the span fields, which makes them a lot easier to use within Datadog.

[codecov]

Codecov Report

Attention: Patch coverage is 0% with 3 lines in your changes missing coverage. Please review.

Project coverage is 88.82%. Comparing base (9160076) to head (ce01478).
Report is 4 commits behind head on main.

Files with missing lines	Patch %	Lines
src/util/tracing.rs	0.00%	3 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #9708      +/-   ##
==========================================
- Coverage   88.82%   88.82%   -0.01%     
==========================================
  Files         288      288              
  Lines       29337    29338       +1     
==========================================
  Hits        26059    26059              
- Misses       3278     3279       +1     

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