[service]: use configured logger whenever possible (open-telemetry#13081)

#### Description

I was using the supervised collector today and ran into an issue where
the agent (collector) was crashing on startup and I wasn't seeing the
logs exported via the configured logger, but I knew it existed bc I was
getting the `Setting up own telemetry...` log.

Turns out in `service.New`, once we've created the logger, we aren't
using it to log and following errors. Instead, they are being returned
by `service.New` and handled by the fallbackLogger.

I propose that, since we have a logger, we use it. 

As a followup it would be nice if any confmap errors could be reported
using the instantiated logger, but that would be a bigger refactor.

#### Testing

Tested locally with the following config:

```yaml
receivers:
  nop:
exporters:
  nop:
  otlphttp:
    endpoint: "${MISSING_ENV_VAR}:4318"
service:
  pipelines:
    traces:
      receivers: [nop]
      processors: []
      exporters: [otlphttp]
  telemetry:
    logs:
      processors:
        - batch:
            exporter:
              otlp:
                endpoint: https://api.honeycomb.io:443
                headers:
                  - name: x-honeycomb-team
                    value: `[READACTED]`
                protocol: http/protobuf
```

console output:

```
2025-05-22T17:25:30.764-0600	info	service/service.go:200	Setting up own telemetry...	{"resource": {}}
2025-05-22T17:25:30.764-0600	error	service/service.go:223	failed to initialize service graph	{"resource": {}, "error": "failed to build pipelines: failed to create \"otlphttp\" exporter for data type \"traces\": endpoint must be a valid URL"}
go.opentelemetry.io/collector/service.New
	/Users/tylerhelmuth/projects/opentelemetry-collector/service/service.go:223
go.opentelemetry.io/collector/otelcol.(*Collector).setupConfigurationComponents
	/Users/tylerhelmuth/projects/opentelemetry-collector/otelcol/collector.go:197
go.opentelemetry.io/collector/otelcol.(*Collector).Run
	/Users/tylerhelmuth/projects/opentelemetry-collector/otelcol/collector.go:312
go.opentelemetry.io/collector/otelcol.NewCommand.func1
	/Users/tylerhelmuth/projects/opentelemetry-collector/otelcol/command.go:39
github.com/spf13/cobra.(*Command).execute
	/Users/tylerhelmuth/go/1.24.0/pkg/mod/github.com/spf13/[email protected]/command.go:1015
github.com/spf13/cobra.(*Command).ExecuteC
	/Users/tylerhelmuth/go/1.24.0/pkg/mod/github.com/spf13/[email protected]/command.go:1148
github.com/spf13/cobra.(*Command).Execute
	/Users/tylerhelmuth/go/1.24.0/pkg/mod/github.com/spf13/[email protected]/command.go:1071
main.runInteractive
	/Users/tylerhelmuth/projects/opentelemetry-collector/cmd/otelcorecol/main.go:57
main.run
	/Users/tylerhelmuth/projects/opentelemetry-collector/cmd/otelcorecol/main_others.go:10
main.main
	/Users/tylerhelmuth/projects/opentelemetry-collector/cmd/otelcorecol/main.go:50
runtime.main
	/Users/tylerhelmuth/go/1.24.0/pkg/mod/golang.org/[email protected]/src/runtime/proc.go:283
2025-05-22T17:25:30.758-0600	warn	envprovider/provider.go:61	Configuration references unset environment variable	{"name": "MISSING_ENV_VAR"}
Error: failed to build pipelines: failed to create "otlphttp" exporter for data type "traces": endpoint must be a valid URL
2025/05/22 17:25:30 collector server run finished with error: failed to build pipelines: failed to create "otlphttp" exporter for data type "traces": endpoint must be a valid URL
```

Proof that the error log exported: 

![image](https://github.com/user-attachments/assets/09ea7f06-bae1-41b8-ad8f-b286bf18e2b5)

Author: TylerHelmuth

.chloggen/tyler.service-log-errors.yaml

@@ -0,0 +1,25 @@
+# Use this changelog template to create an entry for release notes.
+
+# One of 'breaking', 'deprecation', 'new_component', 'enhancement', 'bug_fix'
+change_type: enhancement
+
+# The name of the component, or a single word describing the area of concern, (e.g. otlpreceiver)
+component: service
+
+# A brief description of the change.  Surround your text with quotes ("") if it needs to start with a backtick (`).
+note: Use configured loggers to log errors as soon as it is available
+
+# One or more tracking issues or pull requests related to the change
+issues: [13081]
+
+# (Optional) One or more lines of additional information to render under the primary note.
+# These lines will be padded with 2 spaces and then inserted directly into the document.
+# Use pipe (|) for multiline entries.
+subtext:
+
+# Optional: The change log or logs in which this entry should be included.
+# e.g. '[user]' or '[user, api]'
+# Include 'user' if the change is relevant to end users.
+# Include 'api' if there is a change to a library API.
+# Default: '[user]'
+change_logs: []

service/service.go

@@ -190,17 +190,24 @@ func New(ctx context.Context, set Settings, cfg Config) (*Service, error) {
 	}
 	srv.loggerProvider = lp
 
+	// Use initialized logger to handle any subsequent errors
+	// https://github.com/open-telemetry/opentelemetry-collector/pull/13081
+	defer func() {
+		if err != nil {
+			logger.Error("error found during service initialization", zap.Error(err))
+			_ = sdk.Shutdown(ctx)
+		}
+	}()
+
 	tracerProvider, err := telFactory.CreateTracerProvider(ctx, telset, &cfg.Telemetry)
 	if err != nil {
-		err = multierr.Append(err, sdk.Shutdown(ctx))
 		return nil, fmt.Errorf("failed to create tracer provider: %w", err)
 	}
 
 	logger.Info("Setting up own telemetry...")
 
 	mp, err := telFactory.CreateMeterProvider(ctx, telset, &cfg.Telemetry)
 	if err != nil {
-		err = multierr.Append(err, sdk.Shutdown(ctx))
 		return nil, fmt.Errorf("failed to create meter provider: %w", err)
 	}
 	srv.telemetrySettings = component.TelemetrySettings{
@@ -218,13 +225,11 @@ func New(ctx context.Context, set Settings, cfg Config) (*Service, error) {
 	})
 
 	if err = srv.initGraph(ctx, cfg); err != nil {
-		err = multierr.Append(err, srv.shutdownTelemetry(ctx))
 		return nil, err
 	}
 
 	// process the configuration and initialize the pipeline
 	if err = srv.initExtensions(ctx, cfg.Extensions); err != nil {
-		err = multierr.Append(err, srv.shutdownTelemetry(ctx))
 		return nil, err
 	}