I’d recommend dumping a bucket of water down it to see what happens with the drainage. If it puddles next to the foundation, then (based on the picture) I’d recommend an elbow to shoot it away. If it drains away, then I wouldn’t recommend anything.
Is that the reason the underground drain is plugged or is it just stopped up? Ideally, cleanout that underground drain, but lacking that and given slope away I would recommend nothing. They could breakup the sidewalk and run it under, I guess their not open to sledge hammers and concrete mixers (oh well).
They could cut a trough with a concrete saw, not that hard. I think they want to direct water to the left side of the walkway there, so it would need to be a shallow open drain with a grate.
The other way would be ugly, pipe the water along the wall to the back of the house.
Bob, it does not look like a monolithic concrete slab, it appears like precast pads, texture is different from one side to the nest and the alignment is irregular indicating not all formed at once and inline.
The wide gap inbetween the pavers would also indicate that it was meant for water to drain in the ground.
The building might be 1953, but I would bet that concrete work isn’t.
Pretty much what I am trying to say indirectly Rick, those big gaps should take care of the water from those gutters, but on the other hand we don’t know the area of roof area that is draining through those downspouts.
I think pointing out a potential freezing of the walkway areas during the Winter caused by the gutter downspouts would do for the Inspections.