From what I have gathered, it appears to not be currently possible to create a link group using a workflow action (only "create link"). However, it does seem to be possible using an SDK script. Does anyone have an SDK script to find an existing link group and add entries to it or create a new link group and add entries to it? I'm not great at writing in .NET and would have no clue how to write this myself from scratch, but could tailor a functional example to my needs.
Here are other answers I found that contain pieces of information, but don't exactly answer my question:
Workflow Retrieve Documents part of a Link Group - Laserfiche Answers
Creating a Link Group in Workflow - Laserfiche Answers
How to Create Versions in LFSO09? - Laserfiche Answers
Practicality of relationship links versus Link Groups? - Laserfiche Answers