You should include the Escape Rooms. The Part 4 one you can ignore iirc since its story is basically a sort of retelling of Part 4 with you as the protagonist.
But the Parts 3 and 5 ones are canon. Part 3s Escape Room takes place during their first night in Egypt and the villain Dija Maker was designed by Araki himself. Part 5 is set some nebulous time during Part 5 and is about the gangstars' stands being stolen and needing to free them from containers.
Not an escape room but please consider including NEW Kakyoin's storyline from the Heritage for the future fighting game, it's contextualized in the game as being a dream Kakyoin is having where Death 13 returns to try and kill him again