refactor(greeter): Update auth flows and add configurable opts

- Finally fix debug info logs before dms greeter loads
- prevent greeter/lockscreen auth stalls with timeout recovery and unlock-state sync

quickshell/Common/SettingsData.qml

@@ -294,6 +294,8 @@ Singleton {
     property string centeringMode: "index"
     property string clockDateFormat: ""
     property string lockDateFormat: ""
+    property bool greeterRememberLastSession: true
+    property bool greeterRememberLastUser: true
     property int mediaSize: 1
 
     property string appLauncherViewMode: "list"

quickshell/Common/settings/SettingsSpec.js

@@ -154,6 +154,8 @@ var SPEC = {
     centeringMode: { def: "index" },
     clockDateFormat: { def: "" },
     lockDateFormat: { def: "" },
+    greeterRememberLastSession: { def: true },
+    greeterRememberLastUser: { def: true },
     mediaSize: { def: 1 },
 
     appLauncherViewMode: { def: "list" },