I think I'd remove the corner piece on the left of the refrigerator and put in a floor to ceiling narrow pull out pantry on both sides of the refrigerator. That way, you can keep the closet and move the refrigerator slightly left to allow the door to open fully. The refrig will be "built-in" and no clutter in the corner.

I love your idea of moving things left. Thanks! There's a floor grate though that I'm worried about. Is there a fix for that?

If you put the pantry cabinets on a plinth, the floor grate will be just in front of that I expect. Aren't there sort of detour thingies available for floor vents that will allow the air go through a plinth if necessary? I'm sorry, not English, so I'm struggling a bit ;-) But I had the same idea as Darzy, move the fridge over to the left and fill the space to the right of the fridge with a narrow (pull out) cabinet. Or floor to ceiling narrow cookbook shelves. Probably not the ideal place to store your wine, otherwise you could have a floor to ceiling cubby hole wine rack.

Your new fridge will be wider than the current one, so if you place it to the left as far as possible, you can have a bit more space to the right for a somewhat wider cabinet.

Pull out pantry on a plinth: