I installed Dropbox on a Fedora 32 VirtualBox VM today. It installed without errors and is busily trying to use up all my diskspace synching 360 GB onto my 110 GB virtual drive. I'm not overly concerned because I can delete the VM and start over but I need to be able to limit the directories synched to that VM.
When I open Activities and click the Dropbox icon, nothing at all happens. There's no UI where I can selectively sync, or do anything else, for that matter. I have restarted the VM multiple times. I do get notifications from Dropbox about the thousands of files it keeps copying and in system settings there's a single setting for Dropbox to enable or disable notifications.
First of all, are you really need install Dropbox application on your Fedora, once you're running it on virtual machine (VirtualBox actually)? It's much more convenient share your host's Dropbox folder (either at all or particular part of directory tree) to the virtual machine. I'm assuming you have installed Dropbox application on the host OS. In such a way you don't need additional space at all.
When I open Activities and click the Dropbox icon, nothing at all happens. There's no UI where I can selectively sync, or do anything else, for that matter. ...
As you have notice already, Dropbox application GUI is pretty restricted on Linux. 🧐😧 Unfortunately Dropbox doesn't care much and Linux support is the last resort. Anyway... Selective Sync is accessible on same place in Preferences. "Preference" is accessible only through Dropbox context menu on the icon in system tray. I have made a proposal directed for improved accessibility to some extent, when for some reason the icon is inaccessible. You can vote it up, If you want.
Hope this gives useful directions.
PS: As an alternative you can use command line to set up Selective Sync.
The reason for having the VM with its own copy of limited directories from Dropbox is to keep the regular computer environment isolated as much as possible from the VM. I use NordVPN proxy and some (many?) sites won't accept connections from VPN servers. I use the VM for surfing to those few sites that I care enough to connect without a VPN. If I have to download from those sites, I thought it would be helpful to have a Dropbox directory to store to.
Your suggestion to use a shared directory to the host, though, is a good idea and simpler than messing with Dropbox so I think that's the best solution for now - which is a sad statement for the Dropbox product I pay dearly for each year. It seems rather elitist on their part to ignore the low-cost platforms such as Linux and Raspberry Pi when there are great GUI frameworks that are platform agnostic.