I know that this is also broken in Chrome, so it may be a long shot. However, things worked the way one would expect in Muon (sort of) so I’m going to request it anyway.
I use pinned tabs to keep my mail and other web apps available, and open automatically when I start the browser.
Pinned tabs in macos are not persistent if you close the Brave window with the pinned tabs on. They are persistent if you quit Brave without closing the window. This is annoying since I often just close my browser windows to clear them out of the way. This is the case whatever the On-start up setting is set to.
In Muon the pinned tabs persisted between all the windows - so if I opened a new window, or “tore off” a tab to create a new window, then all my pinned tabs would appear in the new window too, meaning multiple instances of the same page. That probably wasn’t particularly efficient use of my system resources, but it was closer to how pinned tabs work on browsers in Windows.
Right now I’m not exactly sure what the point of pinned tabs are, since it is so easy to lose them.