Have you tried simply rebooting your iPhone and MacBook Pro? The reason I ask is because I am running the latest dev beta for my devices and continuity works with all of them. It even worked with the previous OS versions.
I also updated both my iMacs to Mojave and my continuity features are working perfectly on both my machines and my XS and iPhone 8 devices. I always do a couple of reboots after I perform a major update.