ux v1.38.0: binding section — radios + entities checkbox + dropdown

- Virtual / Pick-from-HA radios; Show-entities checkbox with tooltip
  gates device entities (groups/helpers always listed); searchable
  dropdown only in HA mode, auto-opens when empty, closes on pick;
  Save guarded until a binding is chosen; logic untouched
- smoke_binding_ui.mjs (16 checks); marker_stay/controls smokes green;
  TESTING/CHANGELOG same-commit

docs/TESTING.md

@@ -140,6 +140,12 @@ Run the *core flows* (marked ★ below) in each environment at least once per mi
       (explicit ripple color still wins); off/white lights unchanged [auto]
 - [ ] Alarm pulse (v1.27.0): leak/smoke/gas/CO/siren in 'on' pulse a red ring over any
       display mode; clears on 'off'; unavailable never alarms [auto]; reduced-motion static
+- [ ] Binding section redesign (v1.38.0): two radios — Virtual / Pick from
+      the HA list — with a "Show entities" checkbox (tooltip) next to the
+      second; the dropdown (search inside) appears only in HA mode, opens
+      itself when nothing is chosen, closes on pick; Save is blocked until a
+      binding is chosen in HA mode; groups/helpers listed always, device
+      entities only with the checkbox; editing pre-selects everything [auto]
 - [ ] True dashed boundary (v1.37.3): the open stretch is a REAL dash — the
       rooms' solid strokes are trimmed out beneath it (hover doesn't bring
       them back), walls elsewhere stay solid; the dashes render ABOVE the