Since upgrading my iMAC to Catalina my partner's El Capitan MBAir can no longer see printer.

Make sure you are not restricting the other computer in the Sharing control panel

>System Preferences>Sharing

Toggle printer sharing to On

make sure the printer being shared is ticked on and the users have rights

if that failes

reset the printing system on your partners MBAir

https://support.apple.com/en-us/HT203343

then reconnect to the printer server.

This will erase all other printer connection paths on the computer and you will have to rebuild any other ones that were deleted.

if you don't need a printer server you should connect the printer directly to your network as it's one less point of failure to deal with.

While I do not have a solid solution for the shared printer problem?

see > Share your printer on Mac - Apple Support

I will say that we are also printing from a larger verity of OSs and various devices than we did a few years ago. We have Mac's and an iPad, the kids come over with PC laptops, the grandkids drag in an assortment of school notebooks, iPads, etc.. and the best thing that we ever did was to replace that older shared printer with a new Air Printer. Now we can easily print from any macOS, iOS, Windows or Android device, that we allow on our network without the all the sharing hassles.