I don't think a list of jobs is a dreadful thing per se.
When we had 3 DCs at home I bought a big whiteboard for the kitchen with the DC's chores - eg: whose turn it was to pack & unpack the dishwasher, who's turn to do the bins that kind of thing as well as what everyone was doing that week eg: 'Trevor' rugby practice Weds 5pm, mum take him, MIL collect after collecting 'Sally' from ballet 6:30, mum taking 'Fred' to Cubs Fri 4:30 & collecting 6:30. That kind of thing as well as a space for when we were running out of things so that I could add them to that week's shopping list. I'd also write reminders for me along the lines of 'Fred' opticians Weds 4:00, book 'Trevor' orthodontic appt'.
Sometimes DH would write 'Kids at MIL's for the night Sat- party time for mum & dad!' 😂
However, sometimes I would also leave DH a note to remind him of 'jobs' which would say for eg: please remember to check the downstairs loo as it seems to be running overtime & I think ballcock needs attention, or please remember to fix the shelf in 'Trevor's' room before it comes completely off the wall. If I didn't do that I'd be the one running 3 kids to their various activities, working, cooking, household admin etc & he would conveniently 'forget'. But these didn't go on the family whiteboard as this was between him & me & merely as a reminder for him.
His memory is going now, he likes to do the cooking, but will often make 2 meals, he will forget that it's bin day tomorrow, even though he's asked & I've reminded him several times, he will feed the dog twice. So I've bought a whiteboard that sticks on the fridge. At the top I've written 'Never forget that you are the love of my life' and underneath I will write what is happening today (eg: me working, bins need to be put out, any visitors), what we've decided to eat today, when I've fed the dog.
However, I do think this 'Sarah collect my dry cleaning' Sarah do this, that & the other is rather passive aggressive & treating OP rather like a servant. I'd have tackled my DH about it by now & asked what is going on.