Show fingerprint on lock screen and polkit, gated by lid state

Bring the fingerprint affordance to the Quickshell lock screen and polkit
dialog, matching what hyprlock did on master.

Lock screen: render the md-fingerprint glyph inside the password field's
right edge when a sensor is enrolled, reserving space so long passwords
never run under it.

Polkit dialog: show one method at a time. When a sensor is enrolled and
the reader is reachable, the dialog is just the centered fingerprint icon
(square card); the moment PAM asks for a password it switches to the
password field. Detects pam_fprintd anywhere in the auth stack now that a
gate can precede it.

Lid awareness: a closed lid means the reader is unreachable, so both
surfaces fall back to the password. polkit gets a pam_exec clamshell gate
(auth [success=1 default=ignore] before pam_fprintd) so a shut lid drops
straight to the password prompt instead of blocking on the reader for the
pam_fprintd timeout; the lock screen hides the icon and skips scanning.

The gate points at the fixed /usr/bin path the package always provides so
it survives switching between package installs and dev-link. A migration
adds the gate for existing fingerprint setups.

New helper omarchy-hw-laptop-closed (pure lid state); omarchy-hw-clamshell
now composes it with the external-monitor check.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

shell/plugins/lock/Service.qml

@@ -22,6 +22,9 @@ Item {
   property bool fingerprintAuthenticating: false
   property bool passwordPamConfigured: false
   property bool fingerprintConfigured: false
+  // Lid shut → the reader is unreachable, so hide the affordance and don't
+  // bother scanning; fall back to the password like the polkit dialog does.
+  property bool laptopClosed: false
   property bool previewVisible: false
   property string enteredPassword: ""
   property string pendingPassword: ""
@@ -34,6 +37,8 @@ Item {
 
   readonly property bool locked: lockRequested || sessionLock.locked || sessionLock.secure
   readonly property bool authenticating: authenticatingPassword || fingerprintAuthenticating
+  // Fingerprint is only offered when a sensor is enrolled and the lid is open.
+  readonly property bool fingerprintAvailable: fingerprintConfigured && !laptopClosed
 
   function realScreenCount() {
     var screens = Quickshell.screens || []
@@ -82,6 +87,10 @@ Item {
     if (!fingerprintCheckProc.running) fingerprintCheckProc.running = true
   }
 
+  function refreshLaptopClosed() {
+    if (!laptopClosedProc.running) laptopClosedProc.running = true
+  }
+
   function logEvent(event) {
     lastEvent = event
     lastEventAt = new Date().toISOString()
@@ -115,6 +124,7 @@ Item {
     Qt.callLater(function() {
       root.refreshBackground()
       root.refreshFingerprintStatus()
+      root.refreshLaptopClosed()
     })
 
     return true
@@ -182,7 +192,7 @@ Item {
   }
 
   function startFingerprint() {
-    if (!lockRequested || !sessionLock.secure || !fingerprintConfigured) return
+    if (!lockRequested || !sessionLock.secure || !fingerprintAvailable) return
     if (fingerprintPam.active || fingerprintAuthenticating) return
 
     fingerprintAuthenticating = true
@@ -197,7 +207,7 @@ Item {
     if (!lockRequested) return
     if (result === PamResult.Success) {
       finishUnlock()
-    } else if (fingerprintConfigured) {
+    } else if (fingerprintAvailable) {
       fingerprintRetryTimer.restart()
     }
   }
@@ -245,7 +255,7 @@ Item {
         anchors.fill: parent
         backgroundPath: root.backgroundPath
         backgroundVersion: root.backgroundVersion
-        fingerprintConfigured: root.fingerprintConfigured
+        fingerprintConfigured: root.fingerprintAvailable
         authenticatingPassword: root.authenticatingPassword
         failureMessage: root.failureMessage
         failedAttempts: root.failedAttempts
@@ -275,7 +285,7 @@ Item {
       anchors.fill: parent
       backgroundPath: root.backgroundPath
       backgroundVersion: root.backgroundVersion
-      fingerprintConfigured: root.fingerprintConfigured
+      fingerprintConfigured: root.fingerprintAvailable
       authenticatingPassword: false
       failureMessage: ""
       failedAttempts: 0
@@ -324,7 +334,7 @@ Item {
 
     onError: function(error) {
       root.fingerprintAuthenticating = false
-      if (root.lockRequested && root.fingerprintConfigured) fingerprintRetryTimer.restart()
+      if (root.lockRequested && root.fingerprintAvailable) fingerprintRetryTimer.restart()
     }
   }
 
@@ -356,8 +366,19 @@ Item {
     stdout: StdioCollector { id: fingerprintCheckStdout; waitForEnd: true }
     onExited: {
       root.fingerprintConfigured = String(fingerprintCheckStdout.text || "").trim() === "yes"
-      if (root.lockRequested && root.fingerprintConfigured) root.startFingerprint()
-      else if (!root.fingerprintConfigured && fingerprintPam.active) fingerprintPam.abort()
+      if (root.lockRequested && root.fingerprintAvailable) root.startFingerprint()
+      else if (!root.fingerprintAvailable && fingerprintPam.active) fingerprintPam.abort()
+    }
+  }
+
+  Process {
+    id: laptopClosedProc
+    command: ["bash", "-c", "omarchy-hw-laptop-closed && echo closed || echo open"]
+    stdout: StdioCollector { id: laptopClosedStdout; waitForEnd: true }
+    onExited: {
+      root.laptopClosed = String(laptopClosedStdout.text || "").trim() === "closed"
+      if (root.lockRequested && root.fingerprintAvailable) root.startFingerprint()
+      else if (!root.fingerprintAvailable && fingerprintPam.active) fingerprintPam.abort()
     }
   }
 
@@ -425,6 +446,7 @@ Item {
   Component.onCompleted: {
     refreshBackground()
     refreshFingerprintStatus()
+    refreshLaptopClosed()
   }
 
   IpcHandler {
@@ -450,6 +472,7 @@ Item {
         realScreens: root.realScreenCount(),
         passwordPam: root.passwordPamConfigured,
         fingerprint: root.fingerprintConfigured,
+        laptopClosed: root.laptopClosed,
         authenticating: root.authenticating,
         lastEvent: root.lastEvent,
         lastEventAt: root.lastEventAt