refactor(log): replace stdlib log with the application JSON logger

Every log.Printf/Fatalf becomes a structured slog call through
internal/log: request handlers use the request-scoped logger
(applog.FromContext, carrying request_id), startup failures exit via a
fatal() helper that still emits JSON, and the seedsample/dumpschema CLIs
bootstrap the same JSON logger. Stale client_test expectations aligned
with the refactored wrapper-call logging (message casing, result attr,
ERROR level).

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

backend/cmd/dumpschema/main.go

@@ -10,11 +10,12 @@ package main
 
 import (
 	"fmt"
-	"log"
+	"log/slog"
 	"os"
 	"path/filepath"
 	"strings"
 
+	applog "geniusrun/backend/internal/log"
 	"geniusrun/backend/internal/store"
 )
 
@@ -26,6 +27,7 @@ type schemaEntry struct {
 }
 
 func main() {
+	slog.SetDefault(applog.NewLogger("info", os.Stdout))
 	tmpDir, err := os.MkdirTemp("", "geniusrun-dumpschema")
 	must(err)
 	defer os.RemoveAll(tmpDir)
@@ -91,11 +93,12 @@ func main() {
 
 	outPath := "../docs/DATABASE.md"
 	must(os.WriteFile(outPath, []byte(b.String()), 0644))
-	log.Printf("wrote %s", outPath)
+	slog.Info("wrote schema doc", "path", outPath)
 }
 
 func must(err error) {
 	if err != nil {
-		log.Fatal(err)
+		slog.Error("dumpschema", "error", err)
+		os.Exit(1)
 	}
 }