Answer: Brother Support stated - Both Big Sur and Monterey No Longer Supported

Unfortunately for this black and white Brother HL-2270dw laser printer, Brother Support stated on the US Support site, there is no further printer driver and software support.. for MacOS Big Sur 11 on Nov 12, 2020 and Monterey 12 on Oct 25, 2021. Last MacOS printer drivers support was Catalina 10.15.

https://help.brother-usa.com/app/answers/detail/a_id/171587?R3ModelID=HL2270DW

https://help.brother-usa.com/app/answers/detail/a_id/176028?R3ModelID=HL2270DW

If you think it is worth your time and with some effort, the only alternative is possibly by configuring the HL-2270dw to "print by email." Personally, if printer still has usable life, donate to a Windows or Mac user with MacOS no further than Catalina, or recycle.