Paint the wood frame as lisedv says, then replace the fluorescent tubes with LED tubes that are made for exactly that purpose.

There really isn't anything that looks as good as what you have that will fit the paint footprint (been there, done that).

The "updated" styles are pretty much all unfortunately integrated LED.

Maybe try painting it white, as finding a non-LED light in the exact size will not be easy.

you could leave the wood framework and add this unit over the top.

Paint the wood or leave it as is.

https://farmhouzelight.com/products/5-light-rectangular-cage-flush-mount-ceiling-light

If only it were four inches longer...

What you have is a surface mount, not a flush mount.

You could fasten a panel to the ceiling to cover the footprint of the existing light. Wood (to match cabinets) or painted white (any slight difference from the ceiling paint won’t be noticeable since it’ll be a separate piece with different texture).

Then hang the light of your choice from that panel.

I was going to suggest some kind of rectangular base even if it is wood stained or painted and then any light you find suitable for that location.

Yes, I was thinking about the idea of fastening a panel to the ceiling, but I am not sure where to get one or how to safely attach it to the ceiling.

Piece of wood, screw to joists, paint.

Wood need only be 1/4” thick unless you are planning on an unusually heavy light fixture in which case 1/2” . Thinner is better, visually, I think.

You can go to a lumber shop, and find a suitable material, and have them cut it to your dimensions. Maybe a piece of Baltic birch plywood or other high grade finish plywood with minimal edge voids. Sand it a bit, fill any edge voids with wood filler or spackle, paint it, screw it to joists.

To find joists, take off the current light fixture, it should be screwed to joists and if there is an electrical box it should be attached to a joist, joists are 16” apart.

It would be good to do this when you have your desired new light fixture ready to install, since you’ll need to cut/drill holes in the wood panel for wires. If you’re doing pendants, then multiple holes.

Paint on smooth wood will look a little different than paint on drywall, so don’t expect the panel to “disappear” into the ceiling.

If all that sounds like more hassle and work than you want, then alternative is go to a paint store and return with lots of sample chips, find the paint that matches, and repaint the ceiling. You will find something very very close, I’m sure.

You could have a handy man, unless you are handy enough and make your own ceiling medallion. Just paint it white and then you can paint the center white and don't have to do the whole ceiling.

Good luck!

If you want downlights, you can always suspend a panel and use wafer lights recessed in the panel.

BeverlyFLADeziner: This looks great! Is this something you can buy ready-made?