There is an outstanding issue on GitHub, but it has been open for over 2 years.
It would be nice to get push notifications to work for Brave, especially in an age where censorship across the Internet is rapidly ramping up. I have the option to use Chrome, but don’t want to because I’m in the process of “purging” all of my Google data (yes, I realize they still hold onto everything)l. My old paranoia has unfortunately become a reality now, and I only expect that things will get worse.