Your Mac is up to date – it's running macOS Sonoma 14.6.1, the latest release of the latest major version.
It looks to me like Brother has stopped providing drivers for your printer. The original system requirements for the printer mention really ancient versions of the operating system – Mountain Lion, Mavericks, and Yosemite.
There is a page of Monterey downloads - and if there was a printer driver there, it might be worth trying, seeing as how there are no pages for Ventura or Sonoma. But there's no driver for the printing function, just a suggestion to use AirPrint. With AirPrint, there's enough information built into the printer that you can print to it without needing to install a separate driver.
About AirPrint - Apple Support
Add a printer to your printer list so you can use it on Mac - Apple Support
Brother - MFCJ775DW
Brother – MFCJ775DW Downloads – macOS Monterey
I can find no mention of AirPrint support either on Brother's product description page, or in Apple's AirPrint Support document, so Brother's suggestion may be a dead end.