Fix caret behavior on input field activation (#2850)

* Fix caret behavior on input field activation

* gui: use private property to stay consistent

---------

Co-authored-by: Paul V Craven <paul.craven@optimizley.com>
Co-authored-by: Maic Siemering <maic@siemering.tech>

Author: 3 people

arcade/gui/widgets/text.py

@@ -584,13 +584,17 @@ def __init__(
     def _on_focus_change(self):
         if self.focused:
             self.activate()
-        elif self.active:
+        elif self._active:
             self.deactivate()
 
     def _on_active_changed(self):
         """Handle the active state change of the input
         text field to care about loosing active state."""
-        if not self._active:
+        if self._active:
+            self.trigger_full_render()
+            self.caret.on_activate()
+            self.caret.position = len(self.doc.text)
+        else:
             self.deactivate()
 
     def _apply_style(self):