First, we need to address the utility part of the lighting. for example is your kitchen underlit at night? Do you read in your living room, have floor lamps? Lastly, I don't see electrical in your dining area have you established you can get it there? Oh and why are there two hanging lights in the entry? HMMM

The kitchen is not underlit at night but I want that eventually, and we have no floor lamps. I haven’t considered adding floor lighting. We can get electrical over the dining table if wanted. I know the lights are weird now - not sure what the people who remodeled were thinking. It’s a challenge for sure!

too bad they didn't leave any room behind the wood . or did they?

this one is different

lighting inside the skylights.

try something like this

or see if you can attach anything to the beams

you could also do a faux beam wrap around your other beam and insert the lighting in it

Im digging the faux beam idea.