Using KDE Plasma, .sqbpro files are not opened by sqlitebrowser (nor by anything else).
Searching the web did not find any mention of sqbpro related to xdg or freedesktop.

It seems that if you add sqbpro to the freedesktop mime-type database, the Linux desktops will eventually pick it up.

This page: https://userbase.kde.org/System_Settings/File_Associations/en
says "The KDE software guesses filetypes using the shared-mime-info database, which is shared with many other software projects. To request a new file type to be added to the database, please, follow the instructions here", and points to
http://cgit.freedesktop.org/xdg/shared-mime-info/plain/HACKING

This might be easier to follow:
https://freedesktop.org/wiki/Specifications/AddingMIMETutor/

More information :
https://freedesktop.org/wiki/Software/shared-mime-info/
https://freedesktop.org/wiki/Specifications/shared-mime-info-spec/