I have mobility problems, Spinal Stenosis. Outside I use either a mobility scooter or else a powered small wheelchair if I am going on public transport.
In my flat I am able to cope pretty well. I do have a trolley to take anything from the kitchen into the living/dining room next to it. Not only does this ensure that everything arrives safely, but gives me support.
When I had my kitchen re-done a few years back, I tried to make it as accessible as possible. No high shelves, boiling water tap (no need for kettle), induction hobs, corner cupboards have swing out shelves, I do not have to kneel down to find items. Easy to clean, non-slip amtico flooring.
Same in my en-suite. Comfort height loo, non-slip amtico floor, folding seat in my shower, all built-in cupboards (makes cleaning floor so much easier). Bi-fold door on this, so if I did fall, i would not block anybody trying to reach me
In my bathroom which is mainly used by guests, I do have a shower over bath, but that bath is much lower and I have a screw on support handle to assist anyone needing to get into it either for bath or shower. Have a good grab rail at shower end.
Hard floor throughout flat (except in my own bedroom) east to clean, mop up spills of any sort, and safe. I do not climb anywhere for anything.
I have several quite serious medical conditions, but am able to live a totally independent life thanks to all the modern equipment. Alexa is also fixed so that should I have a bad fall I can just call out to that machine either to contact my nearby daughgter or even to call an ambulance.