According to the Brother web site the latest software download works with Mac's OS 10.6. That may not work with Sonoma. You have two issues, printing and scanning. It may, or may not print but likely will not scan. I recommend downloading the VueScan app which should enable the scanning process. You can try it for free (it will leave a watermark). It is well supported and I can recommend it. I purchased it and I have no association with VueScan.
You mentioned Wi-Fi. The Brother specifications for this unit require a USB connection. Is it so connected? It would be very helpful if you were more specific as to why is not working with this device. Here is the VueScan link.
VueScan Scanner Software for macOS Catalina, Windows 10, and Linux