feat: add shared UI package auth DI (#5720)

* feat: add shared UI package auth DI

* use refs instead of reactive

* pnpm prepr

* move app auth provider setup to src/providers/setup

apps/app-frontend/src/providers/setup/auth.ts

@@ -0,0 +1,29 @@
+import type { Labrinth } from '@modrinth/api-client'
+import { type AuthProvider, provideAuth } from '@modrinth/ui'
+import { type Ref, ref, watchEffect } from 'vue'
+
+type AppCredentials = {
+	session?: string | null
+	user?: Labrinth.Users.v2.User | null
+}
+
+export function setupAuthProvider(
+	credentials: Ref<AppCredentials | null | undefined>,
+	requestSignIn: (redirectPath: string) => void | Promise<void>,
+) {
+	const sessionToken = ref<string | null>(null)
+	const user = ref<Labrinth.Users.v2.User | null>(null)
+
+	const authProvider: AuthProvider = {
+		session_token: sessionToken,
+		user,
+		requestSignIn,
+	}
+
+	watchEffect(() => {
+		sessionToken.value = credentials.value?.session ?? null
+		user.value = credentials.value?.user ?? null
+	})
+
+	provideAuth(authProvider)
+}