Your Brother Printer is AirPrint compatible, so delete the printer from the Mac and add it again by first making sure the Mac and Brother is connected to the same WiFi network. When you add the printer, under Use you want to choose the AirPrint driver instead of the Brother installed driver. That is also the recommendation by Brother on their website.
If you have a VPN installed on your Mac, try removing it as that will interfere with network connections. Sometimes just turning them off will not help and they need to be uninstalled to test.
As for reverting your iPhone 13 to a previous iOS version, no that is not possible and it never has been supported by Apple for any iOS version. If it is running slow, check your Battery Health at Settings > Battery > Battery Health & Charging. If it is below 80%, it needs to be replaced. The battery on the iPhone 13 is only designed to last 500 charge cycles and if you have not replaced it previously, it is likely way over due and will continue to cause problems no matter what iOS version it is using.