Unfortunately yes. You'll still be able to use your license but once that version becomes incompatible with your OS you won't have a choice but to upgrade. I'm disappointed I won't be able to keep the Dropbox sync in 1Password 8. They did have this survey to gauge interest in self hosting it: https://survey.1password.com/self-host/
You can sync local vaults any which way. I personally use Syncthing, but any file syncing service would work.
On another note, I've been using 1Password for years, for free. The mobile app can edit local vaults without signing in, and the desktop program can view local vaults in read-only mode. If I want to edit or add a password, I do it on my phone—it's not worth $150+ to be able to do it on my PC a few times a year.
I don't have the old version installed anymore in order to check, but I thought that 1P only required that you authenticate to Dropbox (since the app just uses the Dropbox API for polling and to pull down changes), not that you turn on syncing. I mean, it's possible Dropbox is so sick they count a signin as a new device, but that would be a grave disappointment
Interesting, because in the root of my Dropbox is ".ws.agile.1Password.settings" which is a plain text file containing the "Dropbox App" path of "Apps/1Password/1Password.opvault" and my understanding of that "Apps" folder in Dropbox is that integrations can write whatever they like to it, but not write outside of it
I have a similar Apps folder for "O'Reilly" from back when I connected their app to Dropbox, and one for Joplin. It's too bad I don't have 1P 7 on my machine anymore, because I no longer have Dropbox on my machine so it would be a good test to see if it still syncs without the Dropbox client present