The way that the arrangements sound like doesn't seem to me to represent different themes for the pause menu. Assuming that the evidence that these were themes were the filenames, i suggest that these themes were situational. One after the other, they increase in intensity and speed. Could be that these were meant to be for when you were in a calm (Franklin), or pressuring (Michael), or action (Trevor) setpiece as a way to continue the energy instead of abruptly stopping the action when hitting the pause button. I think that the reason why they didn't implement it was because playtests probably liked it more that they could take a break from the action whenever and hear the calming music whenever they hit the pause button. Afterall, that's the point of the pause button.
while I would've loved hearing different pause menu themes, Michael's sounds unfinished, and Trevor's sounds a bit too loud with the drums, it's not as chill as the one we got (which is Franklin's original theme)
Franklin, Michael, and Trevor had their same themes in current version in Beta Franklin, Michael, and Trevor had their own themes like the Mission Passed and Menu
