fix(settings): keep Steam ID as string and store the new token

Number("76561198005679788") is 76561198005679790 in JavaScript, so the wrong
Steam ID was saved. The Steam ID now stays a 17-digit string. Theme and
language saves no longer send steamId 0. After a save the new token from Auth
replaces the old one.

Add Vitest and run it in CI.

src/pages/SettingsPage.jsx

@@ -82,7 +82,7 @@ export default function SettingsPage() {
                 reset({
                     useDarkTheme: !!data.settings?.useDarkTheme,
                     language: data.settings?.language || 'en',
-                    steamId: data.steamId ? String(data.steamId) : '',
+                    steamId: data.steamId ?? '',
                 });
             } catch (err) {
                 console.error('Settings load error:', err);
@@ -128,6 +128,8 @@ export default function SettingsPage() {
                 return {ok: false};
             }
 
+            const data = await response.json();
+            localStorage.setItem('tbp_jwt', data.token); // Core reads the steamId from the token
             setFeedback({message: t('SETTINGS.SAVED'), isError: false});
             return {ok: true};
         } catch (err) {
@@ -143,7 +145,7 @@ export default function SettingsPage() {
         await persistSettings({
             useDarkTheme: next,
             language: i18n.language,
-            steamId: profile?.steamId ?? 0,
+            steamId: profile?.steamId ?? null,
         });
     };
 
@@ -153,7 +155,7 @@ export default function SettingsPage() {
         await persistSettings({
             useDarkTheme: isDarkMode,
             language: next,
-            steamId: profile?.steamId ?? 0,
+            steamId: profile?.steamId ?? null,
         });
     };