I have been trying to use Sidecar in the public betas of macOS Catalina and iPadOS 13.
I have a 2019 Macbook Pro, and a 3rd generation iPad Pro, so I know I have supported devices.
Both devices are on the same Wifi network, and both have Bluetooth enabled.
Both devices are logged into iCloud with the same AppleID.
Both devices have two-factor authentication enabled.
I have tried this both with and without a USB-C cable connection between the two devices.
The Sidecar preference pane in System Preferences does appear, and when I go into it I can see in the "Select Device" dropdown that my Mac can "see" my iPad Pro.
However, when I try to connect to it, I get the following after a pause:
I keep watching this page for troubleshooting tips, but none have been useful for me thus far.
FWIW, I have been a "good citizen" and reported my problems to Apple via the Feedback Assistant apps on both devices, so in case this is a temporary bug, I've reported it. I'm just asking here in case someone else has encountered this issue.
Edit: Eventually, Sidecar started working for me (sometimes) after some of the later public betas came out. I'm not sure exactly which version(s) of Catalina and/or iPadOS made the difference for me. So far it has worked without any timeouts in the final versions. I didn't need to downgrade and then re-upgrade as the submitted answer suggests, although I'm glad that has worked for some.
Best Answer
I had this problem setting up a new computer. For me, what fixed it was going into
Settings > Accounts > iCloudand checkingKeyChainIt said I needed to update my account security and prompted me with a few security questions. This seems to have indirectly solved the problem; perhaps some minimum standard of security was not upheld and was causing quiet failure.
Unfortunately, I'm guessing that this won't solve everyone's problems as it seems to be a pretty generic message as mentioned above, just thought I'd add my solution to the pile for everyone who's going down the list and trying everything.