Hello! Thanks for reporting. The game uses IndexedDB to save your progress. Therefore, to play with Brave browser, you will need to go Shields Down to play. In a later build, I will look into a solution which allows you to play, but unfortunately no progress will be saved between plays. The desktop build will be released at the end of the jam.
If there is some other issue after going Shields Down, then it would be helpful to know if there are any items logged within the developer console.