chore: replace console.log with structured logging (#141)

- Add startup logger (utils/logger.ts) with LOG_LEVEL support
- Add ServiceLogger type for scheduler functions
- Replace all console.log calls with leveled log methods
- Downgrade verbose scheduler info logs to debug level
- Remove unnecessary console.log in auth plugin

backend/src/utils/logger.ts

@@ -0,0 +1,46 @@
+/**
+ * Simple startup logger that respects LOG_LEVEL environment variable.
+ * Used for code that runs before Fastify is initialized (db/client.ts, migrations).
+ * Once Fastify is running, use app.log instead.
+ */
+
+const LOG_LEVELS: Record<string, number> = {
+	silent: 60,
+	fatal: 60,
+	error: 50,
+	warn: 40,
+	info: 30,
+	debug: 20,
+	trace: 10,
+};
+
+function getLevel(): number {
+	const envLevel = (process.env.LOG_LEVEL || "info").toLowerCase();
+	return LOG_LEVELS[envLevel] ?? LOG_LEVELS.info;
+}
+
+function shouldLog(level: string): boolean {
+	return LOG_LEVELS[level] >= getLevel();
+}
+
+export const log = {
+	debug(msg: string): void {
+		if (shouldLog("debug")) console.log(msg);
+	},
+	info(msg: string): void {
+		if (shouldLog("info")) console.log(msg);
+	},
+	warn(msg: string): void {
+		if (shouldLog("warn")) console.warn(msg);
+	},
+	error(msg: string): void {
+		if (shouldLog("error")) console.error(msg);
+	},
+};
+
+/** Logger interface for services that receive a logger from the caller */
+export type ServiceLogger = {
+	info: (msg: string) => void;
+	debug: (msg: string) => void;
+	error: (msg: string) => void;
+};