Cycle keyboard layouts alongside composition engines

shell/plugins/bar/widgets/KeyboardLayout.qml

@@ -244,7 +244,9 @@ BarWidget {
     horizontalMargin: 6
     tooltipText: KeyboardLayoutModel.inputTooltip(root.inputState, root.layoutFull, root.multipleLayouts)
     onPressed: function(button) {
-      if (root.multipleInputs && button === Qt.LeftButton) {
+      if (root.multipleLayouts && button === Qt.LeftButton) {
+        root.bar.run("omarchy-input-method cycle")
+      } else if (root.multipleInputs && button === Qt.LeftButton) {
         InputMethodState.cycle()
       } else if (root.multipleLayouts) {
         root.cycleLayout()

shell/plugins/bar/widgets/KeyboardLayoutModel.js

@@ -120,7 +120,8 @@ function inputLabel(state, fallback) {
 function inputTooltip(state, layout, multipleLayouts) {
   if (!state || !state.methods || state.methods.length < 2)
     return layout + (multipleLayouts ? " · Super + I" : "")
-  return (state.name || layout).replace(/^Keyboard - /, "") + " · Super + I"
+  var name = state.current && state.current.indexOf("keyboard-") === 0 ? layout : (state.name || layout)
+  return name.replace(/^Keyboard - /, "") + " · Super + I"
 }
 
 function showIndicator(layoutLabel, multipleLayouts, multipleInputs) {