Why won't my printer connect to Mac after Monterey upgrade?

>Have tried connecting them with a cable, but no luck there either.

Just one question. Does this mean that you have tried to (temporarily) connect the Brother MFC-L2740DW by Ethernet cable to one of the LAN ports of the Wi-Fi router? That would be a good way of ruling out a Wi-Fi printer-to-router problem (for example, a connection to another Wi-Fi network, as mentioned by John Galt). Also, modern dual-band routers often have an alleged "smart" way of discovering devices and selecting Wi-Fi bands, a way that sometimes may lead to difficulties.

AirPrint works with wireless (Wi-Fi) or wired (Ethernet) network connections.

When AirPrint doesn't work, restarting all the affected devices is the gold standard of troubleshooting. The wireless network is an integral part of the communications chain, so restarting it generally fixes things.

On the Mac, removing the printer from Printers & Scanners and adding it again would also be applicable, but there is no functional equivalent for the iPhone.

If the printer isn't there... it simply isn't there as far as the iPhone is concerned.

At this point it seems questionable whether the printer has joined the same wireless network as the other devices. Does that Brother printer have a front panel display that shows it's connected?

Reboot your router.

While you're at it, you might as well do the same with the printer. Power down. Wait a moment or two. Power up again. Wait again. Fixed?

Tried restarting the iPhone also?