Overall of your options, I think I'd pick option 2. Any value in turning the bottom corner with the cabinets? Would the new back door be better further away from the corner so the sofa doesn't foul it?
But to chuck some constructive criticism in, bearing in mind it's so much easier to shoot down other people's ideas than come up with decent ones of my own...
My main issue with option 1 is you have toy storage and sofa squeezed next to each other. It looks to me that it would be hard to play with the toys near the toy storage, which is a big negative for me. Traipsing toys from one area to another... just annoying. And where would they even traipse them to? Not much room to actually play.
Option 2, toys next to the study area also seems not ideal. Of all the areas to keep separate, those 2 would be the pick of them for me. Switching sofa and study area would be one option, but if you did that, I might be tempted to scrap the study area completely in favour of a bigger kitchen table (to use flexibly as study/dining/food prep) and consider using the bottom-most wall for more units & surfaces. You could create a "command centre" type paper/filing system in the corner of the kitchen, so paperwork is easily got out & cleared away. Our small kitchen table often has 3 things at once happening on it, while our other, bigger table sits empty.
I think access to the utility via downstairs loo would not be that weird, and worth it if the payoff is a whole extra wall of kitchen cupboards and surfaces. But swinging baskets of laundry in and out through turns and doors could be very fiddly through small spaces, so you might have to plan it carefully so it's not really annoying in practice.