The aim with both projects (OpenCensus/OpenTelemetry) is the same: having a open source implementation where you can change the exporter (to GCP,AWS,Zipkin,Jeager or anything you want) whenever you like. So Microsoft (or someone else having the API to report data to Azure) could totally implement an exporter for ApplicationInsights. Both projects have a specs [0][1] that are implemented in multiples languages.
Note: OpenTelemetry is just the project that resulted from the merging of OpenTracing and OpenCensus.
[0] https://github.com/census-instrumentation/opencensus-specs [1] https://github.com/open-telemetry/opentelemetry-specificatio...
You can certainly add error-related annotations to traces, however these will typically be sampled.
These APIs/libraries are just the collection part in your app and the actual data can be sent to various backends, like Zipkin, Jaeger, Stackdriver and even ApplicationInsights. Microsoft is also working on making the existing (asp).net APM hooks more extensible to work better with these standards.