MacBook Air can't find Brother MF216W printer

I cannot find a Brother printer with that model number in Apple's About AirPrint device list. In fact I can't find it anywhere, not even on Brother's website.

For now please read Add a printer to your printer list so you can use it on Mac - Apple Support.

Ok, but I still can't find a MF216W in Apple's AirPrint device list. I can't find it anywhere, not even on Canon's website. The closest model designation is Canon MF216n or perhaps Canon MF217w.

I suggest contacting Canon or researching their website to confirm you are using the correct driver, and that it remains compatible with Sonoma. Apple has only incorporated native support for AirPrint-devices for a very long time now, so if your printer is the Canon MF216n or Canon MF217w then all you need to do is add it as an AirPrint printer. No drivers are required for AirPrint printers, and no drivers should be installed.

Power down your router. Unplug it and let it rest a moment or two. While you wait you might as well power down the printer also.

Then, plug in the router and let it start up. Power up the printer. Wait a moment or two and then see if you can print a document from the iPad.

printer in question is Canon 216n.

Details matter. A Canon 216n is not the same as a Canon MF216n. I am unable to find any reference to a Canon 216n anywhere, not on Canon's website, not anywhere.

A brother printer? The only brand I can find to match that model number is a Canon.