Also, for each room give him a different toy/game and tell him that he can’t play with that game until you get to that room Because children get bored quickly, do the ‘basic’ in that room - bed, pick up - leave the dusting to when he is napping if he starts to get bored.

Hate to even say this - but a good cartoon channel or video will help - but always keep an eye - in a blink the kid can’t create havoc. Make sure your doors/windows are locked so he dosn’t wonder. If there are steps, make sure you are on the same level as the child.

As a schedule: There are some cleaning chores that don’t need to be done every single day. Determine which those are and do one of those a day. Others have to be done daily - wipe down kitchen (so while he is eating, clean up the kitchen - under his chair put a piece of plastic (if they don’t have one specifically for this, you can make you own by cutting open a large garbage bad or using old newspapers. After he is done eating(more of it on the floor than inside him), just pick up the paper/plastic and throw away. While he is eating, you are loading dishwasher, wiping down counters, etc.

Toilets/showers- while he is playing in the water wiht all his toys - watching him carefully - clean that bathroom- the toilet, sink, etc. After he is done, just spray that shower/tub with a cleaner let it sit while you dry him and once you are done you wash done the tub/shower and voila done - all that is missing is to mop or vacuum the floor - do that during his nap.

Clothes - load laundry the moment you walk in, folding the dry laundry - leave for later when the two of you are in the living room or whereve watching a movie or singling along to a song or while he colors - you can sit, play word games and fold.

I don’t know what else you have to do, so this is all I can think of - hope it helps.
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My daughter is the same way and she responds to positive reinforcement well. Remember to give your child praise for cleaning up.
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