I’m no expert, but I’d shy away from adding any more swag lighting because it would end up being a dusty, cluttered “wire circus” you’d have to clean.
Maybe something could be done with the existing light, like converting it to track lighting, if hard wiring is an absolute no?

Edit: not converted, installed. You may be able to install track lighting where the existing ceiling light is, though typically it would be in the center of a room.

You electrical right there with the boob light , whaich BTW needs replacing. Any 1/2 decent electrician can run the electrical from there for the pendants and use all LED bulbs then one circuit can handele a ton of lighting and not those really ugly bare bulbs and If that is too much money then do a nice LED track light that either curves or articulates to get light where you need it.

A track can go anywhere and this is a good example of one that would be good. Make sure the bulbs are all LED 4000K you will be amazed at how good the space will look.

We had the same issue at our lake house and got one of these from EQ3

We got the first one because it matched the ceiling lights we already had in the kitchen, but I actually prefer the shape of the second one. Three pendants is way overkill for your peninsula, IMHO. Our peninsula is larger than yours and one is enough.