Hi!
Yes, they will run as the did on Mojave..., but Apple wants to move all of them to the new framework System Extensions.
What they intend to do is to deprecate the kind of extensions as they release system extension frameworks of the same type. First of all will be Driver Kit and Network Extensions, so in a future release after Catalina (around fall 2020?) all kext of those types need to be migrated.
There are other kind of kexts (like system monitor ones to display CPU status, voltage, etc) that will be also deprecated after that when they release support for them under system extensions.
So it seems the process will be slow enough to give time to developers.., there are thousands around!
Finally, beta 1 has a couple of bugs on kernel extensions loading utilities (reported on another thread and to Apple) making those extensions explicity allowed to run (AppleKextExcludeList.kext) to not work... This happened on Mojave first betas too, so I imagine they'll fix that before final release.
More about this here: https://developer.apple.com/videos/play/wwdc2019/702/