It's meant to sound sort of like an old 80s/90s future soldier program. There was Land Warrior and the Future Force Warrior program meant to test new infantry technology, and there were various military studies like Project Camelot. Britain also had a now replaced designation system for their military projects called the Rainbow Codes. Blue Steel for example was a nuclear standoff missile and Green Mace was an anti-aircraft gun.
So "Project Landsword" in this universe would most likely refer to the player mech's development program.