qa-page-admin-widgets.php file contains an array named: $templatelangkeys that is instantiated on line 72 (in my source).
$templatelangkeys contains a list of all avaliable pages (or "template" as they're referred to) that is displayed on the Admin -> Layout -> Add Widget page when selecting what template your widget is permitted to appear on.
You also must allow the widget plugin to display on this template through the widget's allow_template() method. (as you have noticed)
I haven't yet found a method to register a new template that references the custom page plugin (and it doesn't appear to do so automativally). If a method does not exist (I hven't found one) then you will need to hand edit the $templatelangkeys array when you want a custom widget plugin on a custom page.
This question was answered on this thread:
Welcome to the Q&A site for Question2Answer.
If you have a question about Q2A, please ask here, in English.
To report a bug, please create a new issue on Github or ask a question here with the bug tag.
If you just want to try Q2A, please use the demo site.
July 25th, 2023: Q2A 1.8.8 released!