Not a lot of space there! If you aren't looking to put anything here, you could bring in some interest with a mirror above the radiator. Alternatively a couple of well spaced decorative  hooks for jackets, but you might have to work hard to 
Keep the area from becoming cluttered.

Your 2nd picture looks as if there's natural light hitting the little wall above the stairway. If so, it should be possible to put shelving or hanging baskets with plants there, above head height - which would make a sterile stair into something more lively, at least as you walk down.

My hall is much the same but it means I have a bigger living room. My neighbours house is the same house but reconfigured differently. They have a bigger hall but their living room is tiny. I know how you feel.

What did you decide to do with that space? Especially how do you manage with guests and your own shoes/coats/bags

There is space potentially under the stairs - the window is quite small for the space and i don’t want the room to feel crowded as you walk in

I have the same entry way. We keep our shoes and coats in the under-stairs cupboard in the living room. A couple of hooks over the radiator could work well for guest coats.

Fold away stairs? Have you watched 'your home made oerfect' on Netflix? Robert Jamison has some wacky cool solutions.

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I love that show - but I’m afraid in this case it would be impractical in view of my parents being elderly and already struggling with the stairs and an upstairs bathroom

I also used the immediate entrance on the living as a kind pseudo hallway with a mini shelf, mirror and rack for storing hats, gloves and helmets.

I this this is the methods I’m more include to - I ve also used the fall as a door

That made no sense sorry - I meant I also used the door as an extended wall - and put up hooks

Perhaps adding glass shelves and perhaps a mirror as this will create the illusion of more space without looking too obtrusive