How high is the ceiling and how far down is the drop of the skylight casing.

The ceiling is 8 feet high and there is another light further down the hall (where there is no skylight) which is in line with it and we will replace as well.

The skylight is another 8 feet up.

Lots of options, just a matter of taste. just search for small ceiling lights and see what you can find. This one looks like it sheds a lot of light.

https://www.lohas-led.com/1-light-glass-flush-mount-ceiling-lightrustic-ceiling-light-fixture-for-closet-hallwaymatte-black-finish-with-clear-glass-shade-p0983.html