feat: add SPA, serve at /app/, update Dockerfile and README

- React + TanStack Router + shadcn/ui SPA under spa/
- serve spa/dist at /app/ with index.html fallback for client routing
- Dockerfile: node build stage for SPA, copy dist into runtime image
- README: document SPA, CORS_ORIGINS env var, architecture entry
- vite base set to /app/, manifest.json paths fixed

spa/src/routes/register.tsx

@@ -0,0 +1,61 @@
+import { createFileRoute, useNavigate, Link } from "@tanstack/react-router"
+import { useState } from "react"
+import { useTranslation } from "react-i18next"
+import { Button } from "@/components/ui/button"
+import { Input } from "@/components/ui/input"
+import { Label } from "@/components/ui/label"
+import { useRegister } from "@/hooks/use-auth"
+
+export const Route = createFileRoute("/register")({
+  component: RegisterPage,
+})
+
+function RegisterPage() {
+  const { t } = useTranslation()
+  const navigate = useNavigate()
+  const registerMutation = useRegister()
+  const [email, setEmail] = useState("")
+  const [username, setUsername] = useState("")
+  const [password, setPassword] = useState("")
+
+  function handleSubmit(e: React.FormEvent) {
+    e.preventDefault()
+    registerMutation.mutate(
+      { email, username, password },
+      { onSuccess: () => navigate({ to: "/login" }) },
+    )
+  }
+
+  return (
+    <div className="flex min-h-svh items-center justify-center p-6">
+      <div className="w-full max-w-sm space-y-6">
+        <div className="text-center">
+          <h1 className="text-2xl font-bold tracking-tight">{t("auth.title")}</h1>
+          <p className="mt-1 text-sm text-muted-foreground">{t("auth.registerHeading")}</p>
+        </div>
+        <form onSubmit={handleSubmit} className="space-y-4">
+          <div className="space-y-2">
+            <Label htmlFor="email">{t("auth.email")}</Label>
+            <Input id="email" type="email" value={email} onChange={(e) => setEmail(e.target.value)} required autoComplete="email" />
+          </div>
+          <div className="space-y-2">
+            <Label htmlFor="username">{t("auth.username")}</Label>
+            <Input id="username" value={username} onChange={(e) => setUsername(e.target.value)} required autoComplete="username" />
+          </div>
+          <div className="space-y-2">
+            <Label htmlFor="password">{t("auth.password")}</Label>
+            <Input id="password" type="password" value={password} onChange={(e) => setPassword(e.target.value)} required autoComplete="new-password" />
+          </div>
+          {registerMutation.error && <p className="text-sm text-destructive">{t("auth.registerError")}</p>}
+          <Button type="submit" className="w-full" disabled={registerMutation.isPending}>
+            {registerMutation.isPending ? t("auth.creating") : t("auth.createAccount")}
+          </Button>
+        </form>
+        <p className="text-center text-sm text-muted-foreground">
+          {t("auth.hasAccount")}{" "}
+          <Link to="/login" className="font-medium text-primary underline">{t("auth.logIn")}</Link>
+        </p>
+      </div>
+    </div>
+  )
+}