I looked into this a while back as had heard that some docs advised taking all together and couldn’t find any evidence that time of day or taking at same time makes a difference- azithromycin definitely needs to be taken with food, ethambutol with or without and rifampin on an empty stomach
I mostly took rifampin on waking and then others with food an hour later, mostly for convenience to be done for the day. Given how slowly the bugs divide/ grow, it seems improbable that you are going to hit them with any particular medication timing so do what is best for your stomach !