Make sure you're running the latest non-beta macOS 11, i.e. 11.0.1 or higher (i.e. go to System Preferences > Software Update, check for updates, let it install). The version of macOS 11 that ships on the new Macs (11.0) is very buggy, and I've seen issues like what you're describing (Finder windows locking up during operations) in it.
That said, I've been using Dropbox for a few weeks on an M1 Mac Mini and M1 MacBook Pro without issues (after updating to macOS 11.0.1 on both machines).
Now hopefully I don't go upstairs and find my Finder all locked up... 😉
Oh, also, it's worth noting that when you first install Dropbox, it will take about 30 minutes or more to sync (even with Smart sync on), and it's best to just leave it to do its thing - it'll use CPU time and not necessarily behave beautifully until it's done. (I have many GB and tens of thousands of files in my Dropbox, using Dropbox Pro, so smaller accounts will probably sync faster). For those reading this after (or before) getting your M1, it's ok to start your sync on macOS 11.0 (I did, and it worked aside from quirky behavior as described above - i.e. sync didn't break or anything), but it's best to update to macOS 11.0.1 first, just to avoid bugs.
In November you said…
If you’re using a new Apple Silicon device, we recommend using this initial build until Dropbox is compatible with Silicon devices in the coming weeks.
This suggests that, as of November, Dropbox was expecting to ship a native Apple Silicon version soon. Today (February 24) it is about thirteen weeks since that post. I just downloaded and installed the latest version. It was 116.4.368, Intel only.
Any update on native Apple Silicon support?
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