I found the information on airline websites rather accurate (n seats left at this price). I guess this comes directly from how it's stored in the back end booking system (0..8, 9+ seats per booking class)

On legacy carrier official websites, not OTA or LCC like Ryanair.

Before or after buying the ticket? If I already have paid and check in online I can pick the seat. But then it is too late already.

If you mean before you bought the ticket, then I don't know. Maybe they are the last ones to be honest here... But I would be surprised if they were

Also, you can get a subscription from a website like Expertflyer and see the backend inventory from Sabre or likes.