ui: read persisted settings before the API key probe (#27365)

The route loads run ahead of the root layout script, so validateApiKey
read the settings store while it still held factory defaults and probed
/props without the stored key. initStores() now hands the same startup
promise to every caller and the chat loads await it before probing.

The one-time admin baseline no longer overwrites a key the user has
already set: on a first visit the config carries factory values only, so
a diverging key comes from the user and wins.

tools/ui/src/routes/(chat)/+page.ts

@@ -1,6 +1,10 @@
 import type { PageLoad } from './$types';
+import { initStores } from '$lib/stores/init';
 import { validateApiKey } from '$lib/utils';
 
 export const load: PageLoad = async ({ fetch }) => {
+	// loads run before the root layout script, so the stored API key reaches
+	// the probe only once the settings store has read localStorage
+	await initStores();
 	await validateApiKey(fetch);
 };

tools/ui/src/routes/(chat)/chat/[id]/+page.ts

@@ -1,6 +1,10 @@
 import type { PageLoad } from './$types';
+import { initStores } from '$lib/stores/init';
 import { validateApiKey } from '$lib/utils';
 
 export const load: PageLoad = async ({ fetch }) => {
+	// loads run before the root layout script, so the stored API key reaches
+	// the probe only once the settings store has read localStorage
+	await initStores();
 	await validateApiKey(fetch);
 };