chore: add api to monorepo

[dyladan]

Depends on #3260

[codecov]

Codecov Report

Merging #3261 (ead8fd3) into main (6111ae0) will decrease coverage by 0.65%.
The diff coverage is 100.00%.

❗ Current head ead8fd3 differs from pull request most recent head 6224c99. Consider uploading reports for the commit 6224c99 to get more accurate results

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #3261      +/-   ##
==========================================
- Coverage   93.29%   92.63%   -0.66%     
==========================================
  Files         203      130      -73     
  Lines        6609     3124    -3485     
  Branches     1390      656     -734     
==========================================
- Hits         6166     2894    -3272     
+ Misses        443      230     -213     

Impacted Files	Coverage Δ
api/karma.worker.js	100.00% <100.00%> (ø)
api/src/trace/NoopTracer.ts	97.29% <100.00%> (ø)
...s/opentelemetry-core/src/platform/node/sdk-info.ts	0.00% <0.00%> (-100.00%)	⬇️
...opentelemetry-core/src/platform/node/globalThis.ts	0.00% <0.00%> (-100.00%)	⬇️
...pentelemetry-core/src/platform/node/performance.ts	0.00% <0.00%> (-100.00%)	⬇️
.../packages/api-logs/src/platform/node/globalThis.ts	0.00% <0.00%> (-100.00%)	⬇️
...emetry-api-metrics/src/platform/node/globalThis.ts	0.00% <0.00%> (-100.00%)	⬇️
...lemetry-resources/src/detectors/ProcessDetector.ts	31.81% <0.00%> (-68.19%)	⬇️
...perimental/packages/otlp-exporter-base/src/util.ts	79.41% <0.00%> (-17.65%)	⬇️
...ckages/opentelemetry-exporter-zipkin/src/zipkin.ts	84.48% <0.00%> (-15.52%)	⬇️
... and 147 more