A quick guide for those who have completed one ending and unlocked one game mode but are confused as to how to unlock the other:

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During the quest "Final Report," there is a pivotal choice. This quest takes place after the quest "Dead Drop." The choices are "Announce your intent to resign/Give Fellemo your two weeks notice" and "Stay with the Grout Bog Spark Barons."

To unlock Freelancer Brawl: Select "Announce your intent to resign," then select "Give Fellemo your two weeks notice," win the negotiation, then win the fight afterward.

To unlock The Bog Expedition: Select "Stay with the Grout Bog Spark Barons" (or lose the negotiation with Fellemo on the other path) and complete the final quest "Overtime," which has one optional negotiation and one final fight.

Hope that helps!