In our case, it's kinda split.
DH pretty much deals with anything to do with mortgage (although I see all the paperwork).
I generally deal with insurances - but it has got muddled recently as health insurance is now through DH work so he does that, I need to check what the travel insurance situation is (I think it might be through work - or else we had an annual policy and that may be due for renewal...), I do house insurance, and we each do our own car insurance (but because, through a historical thing when we dropped from 2 to 1 car, and timing of when we needed to go back to 2 cars later, each now own the car that the other drives - so I get the insurance letter for the car DH drives but he pays it, and vice versa).
I deal with the utility bills - gas, electric, bins etc. I used to also do telephone/broadband, but DH went hunting in a fit of pique when the last one got too slow, and changed to sky so he pays that - and is now hunting again as they have become rubbish. We will then also drop the payment for TV services as we only got that as part of the broadband package.
DH does also pay for Netflix, amazon prime and possibly spotify (I know DH and DD both use spotify, I just don't know if its the free or premium version).
We each sort our own cars (the ones we drive) for tax, insurance, NCT (our version of MOT) and servicing. But will sort the other also if life is too hectic and it needs to get done.
Generally, I have been the main grocery person - DH has done a good bit more in the past couple of years as we have both got much busier, but I tend to be the person who will set up online shops ahead of time etc. DH tends to be the person who goes and orders (online shopping) new school uniform, parts for fixing things, sports equipment etc. as needed. (If I get these things, I tend to be going into real shops).
Meanwhile I tend to be the person doing runs to menders and shoemakers for repairs etc (a lot tend to be near my office or sometimes I am actually repairing myself), although the dry cleaning run is a split activity depending on who will be nearest.
I mostly book medical stuff for DD and myself, DH does his own. But he is as likely to have organised a dentist visit for DD with himself as I am, and he was the one who brought her to the opticians and sorted her glasses.
Cooking is officially a shared activity. The reality is that it is me doing it. When I am away for work, I had been leaving meals that were very easy to make but DH still went to the takeaway. So unless it is in the oven on the timer, I have learned to leave things that are simple but expect them not to be used (long enough dates to use when I am back or freeze). (He's a fine cook, but just has no patience midweek - which drives DD mad as she's become quite a healthy eating person (fussy but pretty healthy) and doesn't want a load of chips....).
Anything to do with presents, cards, wrapping, planning ahead like that - definitely me.