Does the torus one apply to a wrap-around 2D map then? So if the edges don't wrap, the max amount of colors needed is 4, but if the edges do wrap, you could make a map requiring 7 colors?

EDIT: yep looks like it, the leftmost picture under 'snapshots' here is a 2D map of what's on the torus and looking at e.g. the blue band, it touches all 6 others (just barely the cyan and yellow ones with a few pixels of its tips when wrapping between top/bottom): https://demonstrations.wolfram.com/SevenColoringOfATorus/