Just throwing out a few suggestions to check, you'll have to forgive me as I don't use Brave and don't often use Chrome anymore either, so I'm sorta just spitballing here, but...
1) System date and time is correct, right? Pretty unlikely it's completely wrong on 5 whole devices but you never know...
2) Any extensions that you're running in the browsers that could be doing something similar re: cookie storage? Especially if you're using a profile syncing feature across the browsers (like Chrome has, unsure if Brave has something similar) then you could be inadvertently carrying over an overly strict privacy setting in the browser or an extension that's blocking cookie storage or causing them to expire immediately
3) Does it still happen in an incognito/private browsing/etc kind of window? Important to check #2 first as if an extension is causing issues and it has been allowed to run in those incognito mode windows, or likewise an overly strict security setting, that could trip you up there as well then.
