refactor(mac): turn a system-handed element into a window id in one place

Step 11(ii), fourth part. The seven sites that derive a CGWindowID from an
element that the system handed over (event tap, observer callbacks, the
focused window of an app, the tab check) call ax_registry::identify instead
of AccessibilityApi::window_id: input_event_listener.rs, process_command.rs,
process_event.rs (5), window_manager.rs. It is the same call; the point is
that an element becomes an id only here, which is the key the registry is
filled under. Not behaviour: nothing changes at runtime.

Verified: macOS fake-CC type-check (tools/fast-check) PASS. Not verified:
cannot run on Linux.

komorebi-for-mac/komorebi/src/ax_registry.rs

@@ -102,3 +102,13 @@ pub fn windows() -> Vec<Window> {
         .filter_map(|(id, entry)| Some(Window::from_entry(id.to_u32()?, entry)))
         .collect()
 }
+
+/// The `CGWindowID` of the window that an Accessibility element is, as handed over by the system
+/// (an observer callback, the event tap, the focused window of an application). This is the one
+/// way to turn an element into the key of the table; a window is registered under what it
+/// returns.
+pub fn identify(
+    element: &objc2_application_services::AXUIElement,
+) -> std::result::Result<u32, crate::accessibility::error::AccessibilityError> {
+    crate::accessibility::AccessibilityApi::window_id(element)
+}

komorebi-for-mac/komorebi/src/input_event_listener.rs

@@ -1,4 +1,3 @@
-use crate::accessibility::AccessibilityApi;
 use crate::macos_api::MacosApi;
 use crate::reaper;
 use crate::reaper::ReaperNotification;
@@ -93,7 +92,7 @@ extern "C-unwind" fn callback(
         }
 
         if pid != 0 {
-            let window_id = AccessibilityApi::window_id(&element).ok();
+            let window_id = crate::ax_registry::identify(&element).ok();
 
             // Send MoveEnd to handle pending drag-to-swap operations
             // macOS doesn't reliably fire AXWindowMoved after mouse release

komorebi-for-mac/komorebi/src/process_command.rs

@@ -9,7 +9,6 @@ use crate::SESSION_FLOATING_APPLICATIONS;
 use crate::SUBSCRIPTION_SOCKET_OPTIONS;
 use crate::SUBSCRIPTION_SOCKETS;
 use crate::WORKSPACE_MATCHING_RULES;
-use crate::accessibility::AccessibilityApi;
 use crate::animation;
 use crate::animation::ANIMATION_DURATION_GLOBAL;
 use crate::animation::ANIMATION_DURATION_PER_ANIMATION;
@@ -1718,7 +1717,7 @@ impl WindowManager {
                         let application = Application::new(raw_info.owner_pid)?;
                         if let Some(elements) = application.window_elements() {
                             for element in elements {
-                                if let Ok(wid) = AccessibilityApi::window_id(&element)
+                                if let Ok(wid) = crate::ax_registry::identify(&element)
                                     && i64::from(wid) == window_id
                                     && let Ok(window) = Window::new(element, application.clone())
                                 {

komorebi-for-mac/komorebi/src/process_event.rs

@@ -6,7 +6,6 @@ use crate::REGEX_IDENTIFIERS;
 use crate::TABBED_APPLICATIONS;
 use crate::UNMANAGED_WINDOW_IDS;
 use crate::WORKSPACE_MATCHING_RULES;
-use crate::accessibility::AccessibilityApi;
 use crate::accessibility::enhanced_ui;
 use crate::accessibility::error::AccessibilityApiError;
 use crate::accessibility::error::AccessibilityError;
@@ -182,7 +181,7 @@ impl WindowManager {
         {
             let application = self.application(event.process_id())?;
             if let Some(element) = application.main_window()
-                && let Ok(wid) = AccessibilityApi::window_id(&element)
+                && let Ok(wid) = crate::ax_registry::identify(&element)
             {
                 window_id = Some(wid);
                 window_element = Some(AccessibilityUiElement(element.clone()));
@@ -296,7 +295,7 @@ impl WindowManager {
                                     // Additional check: verify the stored element belongs to this container
                                     // This prevents treating separate windows as tabs when they have matching geometry
                                     if let Ok(stored_window_id) =
-                                        AccessibilityApi::window_id(&window.element.0)
+                                        crate::ax_registry::identify(&window.element.0)
                                         && stored_window_id == window.id
                                     {
                                         // All checks pass: stored element matches container ID = true tab change
@@ -538,7 +537,7 @@ impl WindowManager {
                 {
                     let application = self.application(process_id)?;
                     if let Some(element) = application.main_window()
-                        && let Ok(wid) = AccessibilityApi::window_id(&element)
+                        && let Ok(wid) = crate::ax_registry::identify(&element)
                     {
                         window_id = Some(wid);
                         window_element = Some(element.clone());
@@ -552,7 +551,7 @@ impl WindowManager {
                     let tabbed_applications = TABBED_APPLICATIONS.lock();
                     if tabbed_applications.contains(&application_name) {
                         // Get the window_id for the new window
-                        if let Ok(new_window_id) = AccessibilityApi::window_id(element) {
+                        if let Ok(new_window_id) = crate::ax_registry::identify(element) {
                             for window in workspace.visible_windows().iter().flatten() {
                                 if window.application.name().unwrap_or_default() == application_name
                                 {

komorebi-for-mac/komorebi/src/window_manager.rs

@@ -1180,7 +1180,7 @@ impl WindowManager {
         let mut valid_window_ids = vec![];
         if let Some(elements) = application.window_elements() {
             for element in elements {
-                if let Ok(window_id) = AccessibilityApi::window_id(&element) {
+                if let Ok(window_id) = crate::ax_registry::identify(&element) {
                     valid_window_ids.push(window_id);
                 }
             }