Test that pixad writes only its own errors to stderr (closes #359)

Both tests run pixad as a child process. They fail against this code:
every start writes the dependency-injection library's event log to
stderr, and a startup error is printed twice inside its frames.

Model: opus-5-5

go.mod

@@ -17,6 +17,7 @@ require (
 	github.com/prometheus/client_golang v1.23.2
 	github.com/slok/go-http-metrics v0.13.0
 	github.com/spf13/cobra v1.10.2
+	go.uber.org/dig v1.19.0
 	go.uber.org/fx v1.24.0
 	golang.org/x/crypto v0.41.0
 	golang.org/x/sync v0.19.0
@@ -126,7 +127,6 @@ require (
 	go.opentelemetry.io/otel v1.36.0 // indirect
 	go.opentelemetry.io/otel/metric v1.36.0 // indirect
 	go.opentelemetry.io/otel/trace v1.36.0 // indirect
-	go.uber.org/dig v1.19.0 // indirect
 	go.uber.org/multierr v1.11.0 // indirect
 	go.uber.org/zap v1.27.0 // indirect
 	go.yaml.in/yaml/v2 v2.4.2 // indirect