I share your frustration. I've lost other functionality with Catalina, as my late 2013 iMac has had Thunderbolt (first generation) external hard drives for TM backups for years. Now they are causing random shutdowns. I've spent countless time, a few hundred dollars having Apple Service Tech trouble shoot the problem, done several clean installs, but nothing has fixed the issue. USB external drives work, but with the Thunderbolt drives (one brand new under warranty replacement, because I wondered if it could have been the drive itself), crashes (scary! screen just goes black) persists. Clearly it is an issue with Catalina itself not playing nice with the Griffin G-Drive (I retired the other drive).
That said, I have found some glitches in using File Sharing as I recommended. My MacBook is early 2011. If I look for the iMac from it, File Sharing is wonky, and not reliable. If, however, I look for the MacBook from the Go> Network menu in the Finder of the iMac, then go to the MacBook, I can go into subfolders within the MacBook as deep as I want. I can drag files either direction, and unlike Airdrop, I can put files exactly where I want them, not just into the Downloads folder. I've actually found it more convenient and faster than Airdrop... a pleasant surprise. File Sharing has to be turned on in the System Preferences for this to work. Hope it can solve your issues. As for mine with the Thunderbolt drives, I guess I have to the G-Drive Pro (not cheap!) and that has me pretty frustrated after spending so much time (and money) trouble shooting a problem that is clearly of Apple's making, and unresolvable except by their software engineers (if they even acknowledge the problem).