[Code Health] include-what-you-use cleanup, part 3

[marcalff]

Contributes to #2054

Changes

Please provide a brief description of the changes here.

• completed cleanup of api/include
• completed cleanup of api/test
• total number of warnings decreased from 142 in branch main, to 90 in this PR.

For significant contributions please make sure you have completed the following items:

• CHANGELOG.md updated for non-trivial changes
• Unit tests have been added
• Changes in public API reviewed

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 87.63%. Comparing base (497eaf4) to head (f50ab87).
Report is 121 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #3004      +/-   ##
==========================================
+ Coverage   87.12%   87.63%   +0.52%     
==========================================
  Files         200      190      -10     
  Lines        6109     5868     -241     
==========================================
- Hits         5322     5142     -180     
+ Misses        787      726      -61     

Files	Coverage Δ
...telemetry/baggage/propagation/baggage_propagator.h	100.00% <ø> (ø)
...ude/opentelemetry/common/key_value_iterable_view.h	94.45% <ø> (ø)
api/include/opentelemetry/context/context.h	100.00% <ø> (ø)
...pi/include/opentelemetry/context/runtime_context.h	97.50% <ø> (-0.09%)	⬇️
api/include/opentelemetry/nostd/function_ref.h	77.78% <ø> (+0.51%)	⬆️
api/include/opentelemetry/nostd/string_view.h	98.08% <ø> (+0.12%)	⬆️
api/include/opentelemetry/nostd/variant.h	66.67% <ø> (ø)
api/include/opentelemetry/trace/noop.h	93.34% <ø> (ø)
api/include/opentelemetry/trace/provider.h	100.00% <ø> (ø)
api/include/opentelemetry/trace/scope.h	100.00% <ø> (ø)
... and 2 more

... and 118 files with indirect coverage changes

[lalitb]

LGTM. Thanks for the PR.