Record Postgres instrumentation errors

[Blacksmoke16]

Is your feature request related to a problem? Please describe

The Postgres instrumentation package, in various places, handles errors by marking the span as ERROR and setting the error message:

opentelemetry-js-contrib/packages/instrumentation-pg/src/utils.ts

Lines 430 to 435 in d519d4b

	if (err) {
	span.setStatus({
	code: SpanStatusCode.ERROR,
	message: err.message,
	});
	}

However is it not clear when the exception actually occurred. This makes it more challenging to debug issues since there is no clear timeline of events.

Describe the solution you'd like to see

The OTEL Spec says:

An exception SHOULD be recorded as an Event on the span during which it occurred if and only if it remains unhandled when the span ends and causes the span status to be set to ERROR.

So I propose that in the places where the spans are being set to ERROR and the error re-raised, we also record the exception via span.recordException(err)

Describe alternatives you've considered

N/A

[pichlermarc]

I think this makes sense given that @opentelemetry/instrumentation-pg was already updated to the latest semconv.
Ref semantic conventions for recording errors https://github.com/open-telemetry/semantic-conventions/blob/main/docs/general/recording-errors.md#recording-exceptions

cc @maryliag (component owner) for a final decision whether to do this or not.

[aryamohanan]

Hi @pichlermarc, @maryliag,

I would like to work on this issue once a final decision is made.

[maryliag]

I think it's a good idea! I will assign it to you @aryamohanan 👍