Jeez folks, he's asking for advice, same as most of us have.
OP - my DH was a SAHD and recently went back to work. His SAHDship did not work because....
He saw himself literally as a dad not the "stay at home" person.
Meaning that although our kids are 11 and 8, and therefore at school 9-3, he was doing little in those hours. So I would come home and - breakfast dishes still undone, kitchen table untidy, hoovering or bathrooms not cleaned for weeks etc.
So I had to come in and start doing housework after 10-13h out of the house earning the income. It made me really resent him as he had basically 6h per day to himself and I think it is fair to do a good share (not all!) of the housework in that time.
Maybe, as an approach....?
Think about how much time your wife gets "off" or to herself. Like in my case I probably spend 6-8h per week in the gym/ training.
So then my H should get that same time, which means, let's say, Friday daytime "off" to meet friends, buy books etc.
The other days, I mean you don't need to be up a chimney, but you should basically be doing jobs to complement your wife's working.
You might assign yourself something like 1-2 tasks a day that must get done, to ensure the bread n butter stuff gets done:
Mon weekly food shop, change beds
Tues clean the bathroom, quick hoover round
Weds reserve for ad hoc life admin, paying bills, buying new sch uniform bits, sorting out forms
Thurs reserve for outdoor jobs or car stuff
I mean that's just made up but you get what I mean.
Then make a rule that before your wife gets home, every day, there is not some immediate housework disaster she needs to deal with before she even sits down, like zero clean plates, toys tipped all over the hall, etc!
Good luck.