feat(sdk): add otel.sdk.processor.log.processed self-diagnostics metric

[cijothomas]

Adds the otel.sdk.processor.log.processed counter to BatchLogProcessor, following the OTel SDK metrics semantic conventions.

Gated behind the existing experimental_metrics_bound_instruments feature flag — bound instruments make this practical on the hot path (~1.8 ns per emit vs ~50 ns with unbound).

Changes:

• BatchLogProcessor emits a counter on every emit() call with three attribute variants: success, queue_full, and already_shutdown
• OTLP examples reordered to set up MeterProvider first (so the processor gets a real meter)
• Shutdown order corrected to tracer → logger → meter
• Design doc added at docs/design/observability.md
• Ignored test added (runs in isolation in CI via test.sh)

Ordering requirement: global::set_meter_provider() must be called before creating the LoggerProvider. Rust's global::meter() returns a snapshot, not a delegate. See the design doc for details.

[codecov]

Codecov Report

❌ Patch coverage is 49.33333% with 38 lines in your changes missing coverage. Please review.
✅ Project coverage is 82.9%. Comparing base (284a37d) to head (b85cf83).

Files with missing lines	Patch %	Lines
opentelemetry-sdk/src/logs/batch_log_processor.rs	49.3%	38 Missing ⚠️

Additional details and impacted files

@@           Coverage Diff           @@
##            main   #3514     +/-   ##
=======================================
- Coverage   82.9%   82.9%   -0.1%     
=======================================
  Files        130     130             
  Lines      27311   27386     +75     
=======================================
+ Hits       22659   22711     +52     
- Misses      4652    4675     +23     

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[utpilla]

Follow-up suggestion (not a blocker for this PR): detect & warn when bound counters resolve to noop

If the user constructs the LoggerProvider before global::set_meter_provider, the three BoundCounters permanently bind to NoopBoundSyncInstrument, add(1) becomes a no-op, and no metric is ever emitted. The user gets no signal — just total == 0. The OTLP examples work around it by reordering setup, but the failure mode is silent.

The current public API can't detect this: MeterProvider is type-erased, doesn't extend Any, and has no is_noop() method. Detecting "was set_meter_provider called?" via a flag isn't enough either — NoopMeterProvider is pub and a valid MeterProvider, so a user can legitimately install it explicitly. We need to ask the actual provider whether it's a no-op.

Proposed addition: defaulted is_noop on MeterProvider

// opentelemetry/src/metrics/meter.rs
pub trait MeterProvider {
    // existing methods...

    /// Returns `true` if this provider is a no-op implementation that
    /// silently discards all measurements. Defaults to `false`; the
    /// built-in `NoopMeterProvider` overrides to `true`. SDK components
    /// can use this to warn at construction when self-diagnostics metrics
    /// would be silently dropped.
    fn is_noop(&self) -> bool { false }
}

// opentelemetry/src/metrics/noop.rs
impl MeterProvider for NoopMeterProvider {
    // existing methods...
    fn is_noop(&self) -> bool { true }
}

Backwards-compatible — existing MeterProvider impls don't need to change.

Usage in BatchLogProcessor::new

let provider = opentelemetry::global::meter_provider();
if provider.is_noop() {
    otel_warn!(
        name: "BatchLogProcessor.SelfDiagnosticsUnavailable",
        message = "BatchLogProcessor obtained a no-op MeterProvider from the global \
                   registry; otel.sdk.processor.log.processed will not record. Call \
                   global::set_meter_provider with a real MeterProvider before \
                   constructing the LoggerProvider to enable self-diagnostics."
    );
}
let meter = provider.meter("otel.sdk");
// ... build counter, bind() three times as today

Benefits

• Catches both the "forgot to set the provider" and "set it after the LoggerProvider" cases — the warning fires whenever the bound counters would silently drop measurements.
• One virtual call at construction; zero impact on add() hot path.
• Works on injected providers too, in case any SDK component later accepts a MeterProvider parameter instead of reaching for the global.
• Reusable by BatchSpanProcessor, PeriodicReader, and any future component that emits self-diagnostics.

Does not fix the late-rebind case (user replaces the global provider with a different real one after construction) — that needs the late-binding global::meter() work already noted in docs/design/observability.md.

[cijothomas]

agree. I think we need to solve the fundamental underlying issue - that is the proper solution!

[cijothomas]

@bantonsson PTAL! thanks in advance.