Does Canon PIXMA MP560 work on Catalina?
There's been a lot of question regarding these Canon Pixma MFPs of late.  The driver was probably a 32 bit driver which is why it worked up to 10.14.x (Mojave).  Typically, printer drivers will work with newer versions of an OS if the print system hasn't changed significantly.
From a Windows side of things, we had Windows XP printer drivers in Windows 7/8 machines without issue.  Likewise, we had Windows 7 drivers that worked flawlessly in Windows 10.  And here on the Mac side of things, there are lots of discontinued printers that has compatible drivers (I have an HP CP2025dn that works flawlessly).
Unfortunately, these consumer based MFPs can be difficult to support.  On the OpenPrinting site  this particular printer is listed as a &quot;Paperweight.&quot;  This means that there's not even a generic driver that you can get that will support it.
However, what you can do is if you can get it working on an older Mac or a Raspberry Pi running Linux where it is supported, you can share it over the network and print to that print server and let it render the job instead of connecting directly.