Count post-shutdown-dropped records as already_shutdown on processor.processed

[cijothomas]

Follow-up to #5472. The batch (span + log) and simple log processors dropped records silently once shut down. This counts those drops on otel.sdk.processor.{span,log}.processed with error.type=already_shutdown, which the semantic conventions define as a valid value for this metric.

Question for reviewers: SimpleSpanProcessor is intentionally left unchanged here — it has no shutdown gate, so it keeps exporting spans after shutdown() rather than dropping them, and there's nothing to count as already_shutdown. Adding a shutdown gate there would be a behavior change (post-shutdown spans would stop being exported). If there's appetite to align it, I'll do that as a separate PR — let me know.

[DylanRussell]

SimpleSpanProcessor is intentionally left unchanged here — it has no shutdown gate, so it keeps exporting spans after shutdown() rather than dropping them, and there's nothing to count as already_shutdown. Adding a shutdown gate there would be a behavior change (post-shutdown spans would stop being exported). If there's appetite to align it, I'll do that as a separate PR — let me know.

If the spec says to do it I'd say lets add it.. don't think it's a big deal

[cijothomas]

SimpleSpanProcessor is intentionally left unchanged here — it has no shutdown gate, so it keeps exporting spans after shutdown() rather than dropping them, and there's nothing to count as already_shutdown. Adding a shutdown gate there would be a behavior change (post-shutdown spans would stop being exported). If there's appetite to align it, I'll do that as a separate PR — let me know.

If the spec says to do it I'd say lets add it.. don't think it's a big deal

I'll send a separate PR for that - its a breaking-behavior change, so its better on its own than clubbing with this PR which is purely self-obs metric fixes.