@leoni1140 I assume you are using Ubuntu Desktop. Were you able to sync on your previous version (20.04, perhaps?) of Ubuntu? What, if any, error messages are you getting?
I ask because I've had no issues with sync in Edge Beta on Ubuntu 20.04. I downloaded Ubuntu 21.04, and then successfully installed 21.04. Edge Beta installation fails entirely (Error: "Failed to install file: not supported") on 21.04. Ditto for Edge Dev. I'll have to investigate that issue and solve it before getting to the sync issue.
If I learn anything, I'll pass it along, but your best bet might be to contact Microsoft Edge Insider Support.
UPDATE: I figured out the problem with installation and successfully installed Edge Beta. It syncs. It took forever to get past the "Setting up Sync" message, but it eventually set up and it works fine. Edge version is 91.0.864.33.