It would be great, if Thunderbird could remember the quick filter setting on a per folder basis. In macOS Mail I can set certain folders to only show "unread" messages (e.g. mailing lists, or daily maintenance emails, etc.) and in others I might only be interested in another subgroup of emails.
Making the quick filter sticky is not what I need there, as different folders need different treatment. For me, this is mostly about only ever showing unread messages in certain folders, but there could be other useful cases.