docs: HA integration section first in README, with HACS buttons and full feature table

- Replaces the old 'New' callout with a proper dedicated section at the top of Features
- Shows all 16 sensors, 6 binary sensors, 5 buttons, todo, calendar, text, 6 services
- HACS and config_flow_start my.home-assistant.io badge buttons

Also: fix dark mode not persisting — _setThemeMode now saves immediately to server .env

assets/js/app.js

@@ -1199,6 +1199,12 @@ function _setThemeMode(mode) {
     s.dark_mode = mode;
     saveSettingsToStorage(s);
     _applyTheme();
+    // Persist dark_mode to server .env immediately (no need to send the full
+    // settings payload — save_settings only updates keys present in the body
+    // and keeps all other .env values intact).
+    const token = document.getElementById('setting-settings-token')?.value.trim() || '';
+    const headers = token ? { 'X-Settings-Token': token } : {};
+    api('save_settings', {}, 'POST', { dark_mode: mode }, headers).catch(() => {});
 }
 
 // Listen to system theme changes (for 'auto' mode)