Pendants, yes. Hanging pots, no. The pots will not only give a cluttered feeling, they are also dust collectors. I would add a cabinet above the refrigerator and, if possible, add more cabinets so they go to the ceiling.
Go through your existing cabinets and see if you can remove some things you don’t use as often as your pots and pans.

I love my pot racks. I have two and soon to add a third.

I will join Sherry in what is sure to be the minority opinion. A nice overhead pot rack is useful and attractive. Pots you use will not collect dust. I think your island would appreciate being topped off with something useful and decorative. I plan on installing a brass bar on the backsplash of my range and hang pots from there.

You could always hang pots from rods installed on the end of your island instead. If on the refrig end, they wouldn’t even be seen from the eating area. I did this with my peninsula and it is definitely a space-saver.

I also love my pot rack. I've have had one for 30 years. I've never had any problems with dirty or dusty pots. I use my pots, they aren't for decoration. They are SS and cast iron and aren't funky looking. There is many things that sit out in a kitchen besides pots that doesn't get dirty because you use them.

I would prefer adding two or three pandants (depending on the pendant size you like) over the island.

If you don’t have them already, I think you should also add some under cabinet lighting for the perimeter. The ceiling can lights seem to light up the walkway, but not really on the countertops where you really need task lighting.

I agree that the pot rack can be a cluttered look. They are practical though! If you are a form over function person, it might be fine for you.

(Eta: I meant vice versa, function over form!)

Imo, they look at home in certain kitchen styles like french country, rustic farmhouse, modern industrial, and I am sure some others.

I used to have a wrought iron one in my country style kitchen. My son’s has one in his extremely rustic cabin. It fit in with my rustic knotty pine cabinets and white appliance country kitchen. I even had the black and white and red COW theme happening! It was in the early 90’s what can I say! 🤣

The problem I had with my pot rack though, was that my pots and pans got pretty ugly looking on the bottoms. You either have to be okay with pots and pans that are not brand new pristine being on full display or be a very diligent pot scrubber. I got over it, since it was so practical.

Copper pots hanging on a wall rack like this looks nice, but do the people really use the pots or are they just there ”for pretty”? That narrow wall to the right of the fridge could work.

If this was my house, I would just hang your large painting up higher (seems too low to me anyways) and add a beautiful freestanding furniture piece underneath to store the pots and pans in. The width of piece depending on the space you have. You want to make sure the access to the dining table is not impeded too much.

The problem I see here is "our kitchen cabinets are stuffed to the gills". I'll bet you could streamline your existing storage enough to make room for pots and pans.

First off, your base cabinets are all doors, presumably with shelves behind. Adding pullouts will give you better access to the stuff in the lower cabinets. I did this in our new (to us) house:

I like the fact that the cabinet door is attached to the lower pullout, so it acts as a drawer. I also love the trash/recycle pullout.

I'll bet if you took everything out of your cabinets, and got rid of (or stored elsewhere) things that you rarely or never use, you'll free up a lot of space. And I'll bet you have 2 adjustable shelves in al of your upper cabinets. Adding another shelf to each one, and arranging your things so that items of similar height are on the same shelf, eliminates a ton of wasted space.

When you have completed this exercise, let us know if you still need external pot storage.

IMo first address the lighting issue you have too few pot lights that is why you are getting weird shadows . I like all LED 4000K bulbs they keep colors true and feel like bright daylight. I see you have a corner pantry If this was my space I would do a counter depth fridge where th painting is and a nice tall pantry cabinet where hte fridge is now to house all the pots. Make sure the fridge is in an enclosed space so the sides are hidden from the dining space . Then the art hung just below the window and the morror goes out of the space . IMO a nice chandelier over the table is a much nicer look than a bunch of pots hanging down.

I have had pot racks in several of my previous kitchens. As someone who likes to cook, I loved having them within reach. Your kitchen, however, doesn’t have space near the range for a pot rack, meaning it would be in your walkways or too far to be reasonable. It would look odd and out of place in this kitchen.

Before going down the pot rack track, I think it would serve you well to take everything out of the cabinets and pantry , purge and then reorganize. As an example, when we moved, I realized we did not use everything regularly and found a better places to store items. Perhaps you can maximize space in the corner pantry. FYI - We cook mostly at home in a small kitchen.

I loved my wall-mounted pot rack in our pre-remodel kitchen. But in your kitchen, the first thing I would do is look at that pantry closet. With the right shelf configurations and accessories, you can store a lot of stuff in that much space. You should be able to fit a reasonable set of pots and 2 weeks worth of dry/canned goods in that space.

I love having pots hanging within reach ready for action and have always disliked needing to shuffle them around inside a cabinet (not that we have room in our new kitchen, or the old one for that matter). I’ve never had a problem with dust.

I posted about them there https://www.houzz.com/discussions/6319311/kitchen-before-and-after-with-thanks

I don't like the idea of a pot rack in an open kitchen where it is visible from the table and sofa. Empty your cabinets, purge, relocate, organize. If you have over flow, get another piece of storage furniture for under your painting. Yes, you need some pendant lights over your counter.

Peg board on the back of the pantry door?

Looks like you have two closets on the same wall behind the island, could one closet to the kitchen become more kitchen storage for you? I do think pendants would look nice, and there are nice pot racks that actually have lights in them, it could give you a bit of a rustic feel. the pot lights where miss placed in the kitchen so I see how that is annoying for you.

https://www.wayfair.com/kitchen-tabletop/pdp/prep-savour-acuna-2-light-kitchen-hanging-pot-rack-w007094556.html?piid=1297043952

You need working down light, these might not be the right style but I kinda wanted to show you a complete look.

lots of ways to look at it.

You have a legitimate storage problem in that kitchen. Is there any way to add a long sideboard in the dining area to hold dishes and less frequently used items?

I think a pot rack over the island would add a lot of charm and personality to your kitchen. Here’s a few photos with other options to consider as well.