Brother's printer not printing properly, since upset to Ventura 13.1. No updated drive is available

Please define what you mean by "Mixed Documents"?

The Brother support page:

https://support.brother.com/g/b/downloadlist.aspx?c=us&lang=en&prod=hll6200dw_us_as&os=10077

Info about macOS 13 Ventura states:

"We recommend using AirPrint. If your machine does not support AirPrint, download Brother iPrint&Scan from the App Store."

There is also a very new firmware update listed:

11/17/2022 (1.79/1.72)

So are you using AirPrint? Did you try installing the Brother iPrint & Scan from the Mac App Store? Have you updated the printers firmware to version 1.79 / 1.72 released last November?

It's worth trying to see if that makes a difference. AirPrint will work if the printer is attached to the network via either Ethernet or Wi-Fi (if it's an option).

Not so sure how mixed documents would automatically determine the appropriate paper trays. It may depend on what you are printing from as well as the printer drivers themselves. But I see a form feed auto-select setting on my printers instead of a specific paper tray. (Not Brother).

The firmware update tool:

https://support.brother.com/g/b/downloadhowto.aspx?c=us&lang=en&prod=hll6200dw_us_as&os=10077&dlid=dlf104915_000&flang=4&type3=318

Read the instructions on this page and it should be rather simple to upgrade the firmware of the printer. Brother supplies a utility that will detect your printer and download the appropriate firmware for you specific model, install it, etc. Just don't do this during a storm where you may lose power.