Flatten tracer.initSelfObservability into TracerProvider.Tracer (#7205)

- Do not use [side-effect
programming](https://en.wikipedia.org/wiki/Side_effect_(computer_science))
to setup a `tracer`. Make the setup explicit, unique, and local.
- Add the `newInst` function to ensure DRY and scope instrument creation

sdk/trace/provider.go

@@ -5,14 +5,20 @@ package trace // import "go.opentelemetry.io/otel/sdk/trace"
 
 import (
 	"context"
+	"errors"
 	"fmt"
 	"sync"
 	"sync/atomic"
 
 	"go.opentelemetry.io/otel"
 	"go.opentelemetry.io/otel/internal/global"
+	"go.opentelemetry.io/otel/metric"
+	"go.opentelemetry.io/otel/sdk"
 	"go.opentelemetry.io/otel/sdk/instrumentation"
 	"go.opentelemetry.io/otel/sdk/resource"
+	"go.opentelemetry.io/otel/sdk/trace/internal/x"
+	semconv "go.opentelemetry.io/otel/semconv/v1.36.0"
+	"go.opentelemetry.io/otel/semconv/v1.36.0/otelconv"
 	"go.opentelemetry.io/otel/trace"
 	"go.opentelemetry.io/otel/trace/embedded"
 	"go.opentelemetry.io/otel/trace/noop"
@@ -157,10 +163,19 @@ func (p *TracerProvider) Tracer(name string, opts ...trace.TracerOption) trace.T
 		t, ok := p.namedTracer[is]
 		if !ok {
 			t = &tracer{
-				provider:             p,
-				instrumentationScope: is,
+				provider:                 p,
+				instrumentationScope:     is,
+				selfObservabilityEnabled: x.SelfObservability.Enabled(),
+			}
+			if t.selfObservabilityEnabled {
+				var err error
+				t.spanLiveMetric, t.spanStartedMetric, err = newInst()
+				if err != nil {
+					msg := "failed to create self-observability metrics for tracer: %w"
+					err := fmt.Errorf(msg, err)
+					otel.Handle(err)
+				}
 			}
-			t.initSelfObservability()
 			p.namedTracer[is] = t
 		}
 		return t, ok
@@ -186,6 +201,23 @@ func (p *TracerProvider) Tracer(name string, opts ...trace.TracerOption) trace.T
 	return t
 }
 
+func newInst() (otelconv.SDKSpanLive, otelconv.SDKSpanStarted, error) {
+	m := otel.GetMeterProvider().Meter(
+		selfObsScopeName,
+		metric.WithInstrumentationVersion(sdk.Version()),
+		metric.WithSchemaURL(semconv.SchemaURL),
+	)
+
+	var err error
+	spanLiveMetric, e := otelconv.NewSDKSpanLive(m)
+	err = errors.Join(err, e)
+
+	spanStartedMetric, e := otelconv.NewSDKSpanStarted(m)
+	err = errors.Join(err, e)
+
+	return spanLiveMetric, spanStartedMetric, err
+}
+
 // RegisterSpanProcessor adds the given SpanProcessor to the list of SpanProcessors.
 func (p *TracerProvider) RegisterSpanProcessor(sp SpanProcessor) {
 	// This check prevents calls during a shutdown.