You have a 12 year experience with your Sony TV and say it works well. I would buy the same brand again, It will not matter to you LED or OLED.
Personally I would go with a Bravia Sony in your price range, forget the display technology. The Bravia are HDR sets either way and you will love the picture.
I am more partial to the mid to higher end LED sets. They will have brighter screens for brightly lit rooms and you will barely if any, notice any difference if you have an OLED, in fact the difference will be a less bright OLED screen if that TV is in a bright room.
The OLED thing took off because the manufacturers needed something to market and upsell. There is no ground breaking technology out there.
They OLED could, depending on the maker have a wonderful picture in a darker room, no question about it but that is only if its top quality set, with top quality components to give you a long service life. Sony makes both BTW.
If you check out the TV pictures in a store showroom that is not even close to reality, its closed circuit TV with source material you will not have in your home and the store showroom does not "show" how reliable the set will be.