Apple have just pushed out an update to Catalina - the macOS Catalina Supplemental Update.
The description is pretty vague; “The macOS Catalina Supplemental Update includes installation and reliability improvements, and is recommended for all users.”
The update is nearly 1 GB in size, so I’m not sure why this isn’t the 10.15.1 update, but if you’re living on the bleeding edge and have already updated to Catalina, this update may fix some of the bugs you’ve been experiencing.
Get it through System Preferences > Software Update on Catalina 10.15.