WP does all laundry, manages all bills and general organising e.g payment/equipment for clubs, birthday party buying etc. WP also does food shopping/meal planning.
SAHP should absolutely be doing all of this.
The mental burden of all the planning and organisation should not fall on the WP on top of the mental burden of work.
And the laundry cycle should be done start to finish by the SAHP too. It makes no sense to waste good drying weather. If you have a washer and dryer then it makes even less sense - this is not a huge physical effort at all and the person at home should be able to manage the laundry cycle from start (gathering, sorting) to finish (all put away).
The SAHP should also get the children up and organised in the mornings unless this time with the children is valued by the WOHP and there is no stress involved.
Both can tidy, both can load/unload the dishwasher, maybe the WOHP could clean up after dinner?
Gardening is fine for the SAHP but is this something that is done every day?
Tidying and hoovering - SAHP should do this.
Cooking - SAHP should do this, maybe getting a break one weekend day. But the SAHP should do all the meal-planning and grocery shopping. Any eejit can cook what he is told to cook, using ingredients that have been shopped for by someone else. The only effort expended is putting it all in the pot and not burning it.
Seems that the SAHP is treating this role as if the small elements that are done by him are a favour to the WOHP and not an area where a significant contribution should be made?
Many SAHPs do everything that is now shared or done by the WP in the household, and with more children (and younger children plus babies) to take into account. I had five DCs underfoot for the better part of the 2000s. I think the SAHP here is taking the piss.