How can I mount or extract TWRP Nandroid backups in Windows? Every so often, I need to extract files from a backup. I'm aware Titanium Backup can do this, and there are no doubt other apps capable of the same, but I want to do it on my PC where the backups actually reside.

Files with the .ext4.win extension are simple enough -- just open in WinRAR or similar -- but .emmc.win files are another story. Are there any tools to extract, or, ideally, mount .emmc.win files in Windows?
ext4.win is a posix tar archive according to the file command.

The only partitions I have in a TWRP backup that are emmc.win are boot recovery and system. Those are basically the same as boot.img, recovery.img, and system.img but renamed.

These are ext partition images and you can read the contents of them with ext2read tool.