Vlad Well, how is the preference remembered/identified? Why can't the browser simply add entries to the permissions list in the form of "Open [appname]" for each app that wants to open that the user has stored an "always/never" preference for (which is variable but certainly a finite number)?
In the gear menu, there could be a divider below the standard permissions settings, and then list any apps that the user has said the website may always or never open.
Vlad Not clear how would that work as there are two 'axis': one is the domain and the other is apps.
Now I'm thinking maybe this should be split into its own suggestion, but there are a couple ways you could handle this.
The way Brave does it is to have a list of all websites with any kind of stored permissions, and you can click on each one to see all of the saved preferences.
With this setup, you could add the saved settings to the end of the list, just like the gear menu.
Alternatively, the Safari paradigm is to have it organized by permission, so you can see for a given permission what websites have access to it.
In this kind of setup, you could have a section titled "App permissions" or something to that effect, and the list could be organized similar to the App Shortcuts section of macOS Keyboard preferences: for each website with stored app permissions, list all of the stored settings below the website's heading.