Very nicely done - utilised similar space in a 1914 Edwardian split into three suites, retaining the character with inset panels on the doors. left an exposed cubby in a space similar to that where the red basket is in your photo here, or the under-stair bar example earlier, lit from above for an unexpected display of glass art. Good to see creative practicality!

Would be good to use as a sitting area for BBQ's etc, rather than blocking it off with screening. Probably not ideal for storage though, as it looks like it gets damp/wet. I've done one recently (surprisingly similar in many ways) where we are to excavate down to gain extra head height. We will then lay a new slab and use screening to the sides facing the neighbours. We are to also tile the deck above and waterproof it, etc.. It will add quite a bit of usable space to the whole site and house. It'll be used for BBQ's, etc., cheap way to increase the entertainment areas of both thats for sure! You could do something similar depending on budget. Better to update the area and then use it rather than just blocking it off as it will become wasted but valuable space.

i have a problem with the awkward location of stairs that wastes the sunroom, makes the rumpus room difficult to furnish and the front door has a view of the toilet ...beginning with central stairs and potentially modifying doorways to allow for the stairs without having to walk across the rumpus or upstairs living room attempts to avoid the big wide hallways affect without useful locations for furniture ..the rumpus room now has space for comfortable furnishing and private access to a full bathroom and good sized laundry...using the old sunroom for a compartmented bathroom retains the original walls and windows and includes space for a bathtub and shower with big views.. we should always include real scale sized furniture to establish the best walking paths across rooms and my suggestions also retain the size of the original kitchen to keep more of the original walls and ceilings and retains the proportion of the bay window and allows space for an alternate access to bed 3 (preferable the linen cupboard would remain in this location) and consider avoiding the enclosed pantry (would the door ever be closed?) in favour of a more open space for better light and ventilation and maybe a herb garden window box in the bay window with external blinds to exclude western sun.. there's a fridge closer to the outdoors, stacked wo and MW to define the pantry and only a small sink in the island for more useful set down space for shopping and serving meals

everything you've suggested sounds ideal and you will only need to build a frame underneath the stairs to create a wall to the side of the steps and directly under the top step to allow for a door and cover with the same wall lining and either add an electric or battery operated light under the stairs and shelving to suit what you want to store