Hi HannahSHa,
babowa provided you with a link indicating that a macOS 10.5 Catalina driver could be tested. The iPrint&Scan may even work for printing, but with limitations.
Since the HL-2270DW is a network printer, you could perhaps carry out a test with a network connection, if a direct USB connection was used earlier. You have the choice of testing a wireless or wired network connection to a router. A wired network connection would be by Ethernet cable to one of the LAN ports of the router.
Unfortunately, an HL-2270DW does not appear to support Apple's AirPrint technology, so some kind of driver would be needed.
https://support.brother.com/g/b/downloadlist.aspx?c=us&lang=en&prod=hl2270dw_all&os=10060
The HL-2270DW seems to support PCL6, so if nothing else works, you may even want to carry out an experiment with generic PCL printer software from a macOS pop-up menu (see also Use under the Add a network printer by specifying its IP address section in Add a printer to your printer list so you can use it on Mac – Apple Support (UK)).
If necessary, try resetting the printing system and re-adding the printer.
Reset the printing system on your Mac to solve a problem – Apple Support (UK)
As always, make sure that you have backup copies of all important files before testing anything. Software conflicts cannot be ruled out.