It means he's going from one activity to the next activity in a sequence. We could also say "continuing my routine by having breakfast."

Greetings, 'On to ' gives the feeling of movement.So, if we are talking about moving to some other activity from one, we can use 'on to'. Ex- I have finished my work and onto meeting. ex- I am onto new projects. Ex- I have traveled so many places and onto last one now. Regards, Deepika Mantra

Hm... I don't know if it's different in other English-speaking countries, but in the U.S. (at least, in my part of the U.S.) I never hear "on to" being used like that. Occasionally I will say or hear the phrase "move on to [noun]" or "go on to [noun]" in sentences like "Let's move on to today's lesson," or "I'll go ahead and go on to the next question," but that's about it. It's pretty rare, at least where I live.