Copies installed before version 2.7.5 need one manual install to clear this. Open
your purchase page from the Polar order email, download BrainOS again, and drag it
into your Applications folder over the old copy.
macOS ties an installed app to the certificate that signed it, and only lets it
update to a build carrying that same one. The earliest builds were signed with a
development certificate or none at all, so the copy you are running refuses the
properly signed releases that followed — correctly, and with an error about a code
signature failing validation. No version can get past it, because the check runs
inside the app you already have.
Nothing of yours is touched: your notes, maps, habits, chats and settings live in
your Library folder, outside the application. Updates install themselves again
from then on.