Correct installation of the scanner driver: Do not connect the scanner to the computer. Start installing the software first. During installation, a message will appear on the monitor informing you when to connect the scanner to your computer.
To use any computer device, software (driver) is required. It is recommended to use the original software included with the device. If you don't have the software and can't find it on the device manufacturer's website, we can help. Tell us the model of your printer, scanner, monitor or other computer device, as well as the operating system version (for example: Windows 11, Windows 10, Windows 8, etc.).
With that said, you may be able to use the Image Capture app instead of the Open Scanner in Settings. That is the first thing I would try. If the standard ICA driver that is provided with the OS is unable to detect your scanner in Image Capture, then you will need an ICA driver from brother. Since they choose not to support Ventura, you may be able to find it in a different model from Brother. They say it is included with the Printer Drivers that you can download, but don't know if they give you the option to just install the ICA driver without the printer drivers.
I have the same problem with Brother DCP-L2540DW. I am not able to use the scanner with "Brother iPrint&Scan" app. I even downloaded the latest driver from Brother website =us&lang=en&prod=dcpl2540dw_us_as. I can not use the scanner at all.