Thank you for your review! I have just released a new version (2.10.0) that adds support for "chrome://" URLs for the quick bookmarking icon.
Additionally, the URLs starting with "file:", "about:" and "moz-extension:" are also supported on top of the classic "http:" and "https:".
Please note the update may take a bit of time to be available to everyone.
If you want to report another issue or request a new feature, please feel welcome to do so on GitHub at https://github.com/teddy-gustiaux/default-bookmark-folder/issues.
The Mozilla Add-Ons website only allows me to respond once to a review, so it is not the ideal place for a conversation. :)