update examples and getting started for provider and api package

[dyladan]

• Finishes the provider rename in examples and getting started
• Updates examples and getting started for api package update

[codecov-io]

Codecov Report

Merging #750 into master will increase coverage by 4.98%.
The diff coverage is n/a.

@@            Coverage Diff             @@
##           master     #750      +/-   ##
==========================================
+ Coverage   90.88%   95.87%   +4.98%     
==========================================
  Files         233      160      -73     
  Lines       10438     6260    -4178     
  Branches      965      498     -467     
==========================================
- Hits         9487     6002    -3485     
+ Misses        951      258     -693

Impacted Files	Coverage Δ
...in-postgres/opentelemetry-plugin-pg/src/version.ts	100% <0%> (ø)	⬆️
packages/opentelemetry-core/src/common/types.ts	100% <0%> (ø)	⬆️
...kages/opentelemetry-plugin-dns/test/utils/utils.ts	33.33% <0%> (-26.67%)	⬇️
.../opentelemetry-core/src/trace/spancontext-utils.ts	100% <0%> (ø)	⬆️
packages/opentelemetry-core/src/utils/url.ts	100% <0%> (ø)	⬆️
packages/opentelemetry-plugin-redis/src/version.ts	100% <0%> (ø)	⬆️
...pentelemetry-core/src/platform/node/performance.ts	100% <0%> (ø)	⬆️
...ckages/opentelemetry-plugin-ioredis/src/version.ts	100% <0%> (ø)	⬆️
...metry-core/src/trace/instrumentation/BasePlugin.ts	81.57% <0%> (-5.27%)	⬇️
...-plugin-postgres/opentelemetry-plugin-pg/src/pg.ts	91.52% <0%> (ø)	⬆️
... and 187 more

[dyladan]

@open-telemetry/javascript-approvers please review this. Until it is merged examples, getting started, and benchmark are all failing on master.

[mayurkale22]

Added a few comments, looks like we are still using core instead of api module esp. init provider and get tracer.

[mayurkale22]

lgtm