Hello,
we are aware about the fact that Kernel Extensions are deprecated as of MacOS 10.15 Catalina. We are already working on switching to the new Endpoint Security and Network Extension frameworks meant to replace them, however the work is not yet finished. We are working hard to finalise the work and roll to the new code out as soon as possible, but it is not a simple task, so it won't be out in Avast 14.4 for sure.
Unfortunately in the foreseeable future it will be necessary to live with the popups, which AFAIK are supposed to only pop once after each restart.
Kind regards,
Ondrej Kolacek