There is a path to your goal. If you can find a swivel chair you like, you can replace the hydraulic column. This Class Four column with 450lb. capacity can raise 7.6 inches. Link. For counter height seating the seat surface height needs to be 24".

This highlights the comfort problem with island seating for adults when compared to dining table seating. 18" seat height for dining allows leg support with your feet on the floor. They dangle at an island without an added support. A footrest doesn't help that much. Not a consideration for kids. They're feet don't touch for either.

"Everything I am finding that I love has a very small seat."

Be careful what you write, some people read between the lines.

Post an image of the room

I have the Maxine stool from this company. Not a 100% modern/sleek design, but they have a very comfortable seat and back and can be customized with any leather or fabric. I did a standard leather on the seat and a custom fabric on the back.

https://www.jessicacharles.com/Products/Search?TypeID=CSTOOL

Herman Miller has options. Stools - Herman Miller

Stools with wheels are not good for all beverages.

No wheels. Sylvan Synthetic Leather Swivel Counter Stool - Room & Board Modern Commercial Furniture - Room & Board (roomandboard.com)

We have these and we are tall I find I never really lean back when seated at the island you do realize swivel stools with a back will whak your counter edge all the time The back on ours are really just supporting your lower back a bit and slip under the overhang almost since we only have a 12" overhang.

We love our Pottery Barn Madison stools. I didn’t pick the swivel option but it is available. Very comfortable back and low profile.

https://www.potterybarn.com/shop/furniture/seating-collections/maison-collection/

Have you found stools yet? They recently got new stools and chairs at my health club so I snapped some pics this morning. Very comfortable, seem like they'd be easy to clean, and I figure they are likely commercial grade to stand up to heavy use.

Bar stool label:

Chair label:

@chicagoans I haven't purchased anything yet, still on the search! I am now debating if we really need them to swivel or not. The stools you took photos of are very nice, I will give them a search. Thank you so much I appreciate your help!!