feat: implement Phase 1 server-side federation groundwork

Add multi-instance support foundation: shared federation types
(ReplicatedInstance, InstanceInfoResponse, VerifyPasswordRequest),
database schema changes (home_instance, replicated_instances on users,
instance_name on settings), public instance info endpoint, auth
registration with homeInstance and username@domain collision fallback,
password verification endpoint, and replicatedInstances sync on user
profile. Extract duplicated sanitizeUser into shared utility across
8 server files.

packages/server/src/utils/sanitize.ts

@@ -0,0 +1,26 @@
+import type { User, ReplicatedInstance } from '@backspace/shared';
+import { schema } from '../db/index.js';
+
+export function sanitizeUser(row: typeof schema.users.$inferSelect): User {
+  let replicatedInstances: ReplicatedInstance[] = [];
+  if (row.replicatedInstances) {
+    try {
+      replicatedInstances = JSON.parse(row.replicatedInstances);
+    } catch {
+      replicatedInstances = [];
+    }
+  }
+
+  return {
+    id: row.id,
+    username: row.username,
+    displayName: row.displayName,
+    avatar: row.avatar,
+    status: (row.status ?? 'offline') as User['status'],
+    customStatus: row.customStatus,
+    isAdmin: row.isAdmin === 1,
+    createdAt: row.createdAt,
+    homeInstance: row.homeInstance ?? null,
+    replicatedInstances,
+  };
+}