My guess is it was something about legacy system extensions. The Seagate drives will likely still work, you just won't be able to use whatever Seagate software you installed for them. If the software was used to lock or encrypt your drives, then you'll probably want to be looking for alternatives. I'm not sure about the printer, if you can get by without the extension it installed. If it supports AirPrint, then you should be fine. In both cases, check to see if there are any software updates and/or if you really need them installed.
As far as I know, I don't think Apple has announced when they'll no longer work. They've only said they "will be incompatible with a future version of macOS".
Some system extensions aren't compatible with current versions of macOS or won't be compatible with a future version of macOS. Learn what to do if you see an alert about system extensions or kernel extensions.
support.apple.com