Is there a way to batch add multiple files to MKV & just have it automatically run through each file?
Welcome!
MKVToolNix GUI itself is not a tool for batch-processing. However, the command-line tools belonging to MKVToolNix, mostly mkvmerge but also mkvpropedit & mkvextract, definitely are meant to be fully scriptable/automatable. There are examples for various automation tasks available.
Last, there are third-party tools out there that do allow for certain batch operations.