After my first Pfizer (Bio-NTech) shot, did my monthly metric the next day with no ill effects. Second shot I had to cut the ride short to do some yard work, but I can't blame the vaccine for that. (Well, to be honest, I didn't try!)
My experience notwithstanding, it's probably a good idea to plan for a day or two after each shot where you don't have any big/important workouts, rides, or races.