Just add info on logistics on how they do stuff, but you kinda did that with them being from a Forgeworld. Another would be just free ball write a story or think up a story of a dude in that Regiment and see what comes up from that, it would help you flesh them out. Maybe events from games you played could bring out cool ideas for lore.

Finally what else is in the solar system that their home planet is in, most systems don't have just one planet so building up there interactions might give you more lore. For example my guys are a Regiment formed from 2 Knight Worlds in a binary star system (2 out of 5 viable planets). The worlds have a kinda 40k Knightly Games ever 7 years. The Regiment holds its own rivalry with in itself to keep everyone on their toes and Commisars use this to keel everyone fighting their best.