I registered an account just to pass on my thanks for the information found in this thread, and to add some information I found with my own toilet seat.
Mine was a Laufen Pro fitted in (circa) 2007. The seat was listed as "soft close" which, at the time, was somewhat new to toilet seats. I didn't give much regard to how it fitted and let my professional plumber do it. I remember reading the instructions at the time (before they were thrown out) and they said the seat needed to be in a particular angle before it could be lowered into place. This would be the same in reverse were it to be taken off. The angle I discovered later is "flat" as in it is how the seat would be were it in the closed position. This is really obvious when you buy a new one but completely obscured the moment you move the seat.
Like
@Ben-gee said, giving it a bit of extra force is the only way to really get it out after a few years. In my case it had been 15 years, but yes, a strong tug was enough to free one side. The other side wasn't budging so easily but one ear-piercingly loud
CRACK later and I had the seat in a few more easily managed sections!
TLDR Advice to the next person who finds this thread; use brute force and have a replacement loo seat (and fitting) to hand.
(quick edit) for me at least the fitting pegs were unwound with an 11mm straight edged spanner on the top and, even though they are square nuts underneath, a 12mm circular spanner was perfect to capture the nut.