Screens is stuck at "Downloading..."

If you're trying to connect to a Mac and Screens seems stuck, you may need to perform some steps.

Note: these instructions should be performed while you have physical access to your Mac or you may lose access and not able to reconnect.

Reset required services

When this happens, try to switch from Remote Management to Screen Sharing (or vice-versa).

You can then switch back to Remote Management afterwards but make sure that Observe and Control are enabled under Options...

... and that the Mac user is allowed to connect via the Remote Management service.

You can uncheck both options and re-check them back in order to reset them.

It appears that the Remote Management/Screen Sharing service needs a reset after upgrading macOS because something went wrong during the process.

Reset Firewall

If the macOS firewall is enabled, try to turn if off and then back on.