Apple - Weird issues after updating to macOS 10.15 Catalina beta 8 (19A558d)
I was having the same issue, and I just reinstalled the beta by going here: https://developer.apple.com/download/ then clicking "Install Profile" on Catalina. Then went to software update, and it started downloading Catalina again. Everything's fine now (no hanging, dragging works, etc.).
Beta software are supposed to be for testing purposes. Specifically BetaOS is released publicly for tech enthusiasts only and that's absolutely not recommended to install on anyone's primary machine.
It seems like Apple is trying to force use of firewall which is creating trouble for Internet related apps (Chrome, Mail, Safari). You can investigate with following.
0) Fist Check your DNS settings. Sometimes your ISP provided DNS sucks. Use Google DNS (8.8.8.8, 8.8.4.4 etc)
1) Check Firewall and proxy settings in your Settings app.
2) You can investigate your hosts file sudo nano /etc/hosts
(Careful: You need to know what you're doing.)
3) Just assume Apple is outdating your system :D
4) Chances are Apple enabled several Debug Logs to test the Beta 8. they'll turn it off with final release. Investigate using Console.App
5) You can further investigate using Activity Monitor.app
(Both are found under Application > utilities)
That's my best guess :)