Brother MFC-L3770CDW Stops Responding Under Ventura

Since updating to 13.3.1, I'm finding that the Brother MFC-L3770CDW stops responding when opening the scanner in Settings. When I do this, the printer will go from showing as Online to Offline. If I close out of the scanner dialog and perform a test print, it works fine.

If I remove the printer and attempt to re-add it, it finds it over Bonjour, but the driver detection simply goes from Auto Select (which is what it usually selects and detects the printer/scanner/fax) to Generic PCL Printer which works for printing only.

If I remove the printer and either reset the printing system or reboot, I can successfully add the printer again. It will stop working a few hours later.

Everything is on wireless, but I've already been through the process of restarting the router etc., and this behavior only started with 13.3.1.

Windows desktops on the same network are not impacted.