I need you to make a few things clearer to me.
Tested it with cable (OK) and then wifi (not OK).
What cable.. I am guessing USB. Please make that absolutely clear.
When you test with WiFi that is very difficult if you have just configured the printer with USB which makes it a LOCAL Printer.. not a network Printer.
Don't see how to get the screen you showed for Airport Utility -- if I try add device, it says none found.
Is the TC the main router of the network.. if not this job must be done on the main router. Do you have any errors showing on the TC summary? Like double NAT which will mess things up like crazy.
Going back to your configuration of the printer wifi .. how are you doing that? Again I am unclear.
Did you use the USB connection to go into the canon actual printer setup pages and the wireless must be configured to join the wireless router.. NOT adhoc mode. It must use infrastructure mode. Is that how you did it? Or did you use WPS.. I see the main instructions from Canon say the wireless is setup by WPS.
https://ugp01.c-ij.com/ij/webmanual/Tutorial/TS3100%20series/EN/TRL/trl-3000-a.html
Printer Sharing on.
If you mean on the Mac printer setup.. No.. as soon as you turn on print sharing you totally mess up the network. Even wifi (if setup properly may not work) because it is looking for the computer and sending print jobs to the computer not the printer. Print sharing is ONLY used for a USB printer with NO WIFI CONFIGURATION. And it is only for other computers on the network to send jobs to the USB printer plugged into the computer. But if your Printer has WiFi it has an inbuilt print server and you should not send print jobs via another computer computer on the network.
Start over.. remove the printer from all the computers again. Make sure NONE have sharing turned on. Reset the printer to default.. You will need to read the manual to know how to do that.
Now only do the setup on the Mac Mini.. Until it works on the mini forget all the other computers.. none of them will work because you are not configuring the printer to the Time Capsule.. The printer will appear pretty much automatically on all the other computers via bonjour once it is part of the network.
Only do wifi setup.. although I understand if that is difficult.. use the WPS instructions .. Time Capsule has WPS but accessed only via the airport utility here. With the setup open go to Base Station and Add WPS printer.

Do not use pin method.. always use first attempt.

Trigger WPS on the printer and within a few seconds it should work. Note printer needs to be close to the TC so it has excellent wireless signal at least during the setup.
If it works properly the printer will appear as a client in the TC.
Make sure the TC is actually seeing the printer.. or use the printer test page to print out its current network configuration which will include the IP address.
That is the IP you must reserve in Airport Utility so it never changes. This can be left until last.. it is more important that you can print to it now.
You should now test. If it does not work.. open Terminal and type
ping printerIPaddress .. Where printerIPaddress is IPv4 address of the printer.. like 10.0.1.10
If ping responds then we might need to dig deeper.. but if ping does not respond you have no network connection to the printer and need to start over.. sorry. Or buy an AirPrint capable printer which are far easier to get working in my experience.
It will help me tremendously to give me your actual network setup.. with all the IP addresses.. and hopefully you can show which client is the printer and what IP it is getting. Screenshots of the entire network setup.
I went looking for Bonjour and found that iStumbler can detect it. Apparently those @Martin's MacAir etc alternative names are already set up as IPP. At least this screen shot suggests it's been setup:
I think this is wrong. and show you are configuring the Printer as ad hoc.. and not infrastructure mode. i.e. the printer is expecting clients .. whereas the printer should be a client on the router.
This is why ethernet is so much better.. if the printer has ethernet plug it into the TC.. and it will work about 200% better.