IPP is a universal printer protocol aka “print anywhere”. Some printers support it natively, some need some help from a PC. If that PC runs Linux the most likely method is to run CUPS and connect it to the printer over USB.

By IPP autodiscovery, do you mean mDNS? If so, does the router needs to install avahi as well for single-network discovery to work? Or just the client?

Yes the autodiscovery is done with mDNS, which on Linux is done with Avahi.

Typically Avahi is needed if you consume services over mDNS or provide them.

So the Linux clients need Avahi. But the router only needs Avahi if the printer is connected to it, or to propagate broadcasts across zones.

I’ve thought users could just manually input the IP addresses

You can, but it’s really nice to have the printer available automagically (on any OS).

BTW one extra potential benefit of solution 3 might be that the “printer” would always appear to be present on the network and accept print jobs, even if the actual printer is off, because the Pi running the print server would actually be on. Otherwise if the printer itself is providing the connectivity and announcement it will not appear in the list when it’s off. Whether you consider this a plus or not depends on how you handle your printers, I turn mine off when not in use, but some people let it go into powersaving mode so it’s always ready to print.