OP you have an unusual attitude. You seem to think that your life has been extraordinarily hard and that other people’s are extraordinarily easy.
For example I find your attitude in the quote above very naive - a property that “you’d just never, ever sell”. Of course loads of people would choose to sell an inherited property abroad. Keeping it would involve working with letting agents, builders, project management, paying bills, managing tax in another country with language and cultural barriers. They also needed liquid cash - and lots of it- for renovations. Perfectly reasonable choice to sell.
Your attitude to the values they got for their properties is also naive. Yes house prices have risen, they have always risen but it’s always a lot of money at the time. Most people who have ever sold property have the “wow look what it would be worth” conversation 20+ years later - they still enjoyed the money.
I think when some people are saying that they would “help” their kids and can’t understand when other people don’t might be overlooking that you were not asking for 10% of a 200k flat in a town. You seemed to want 100% of a flat in London - what’s that 500k? And as you have said you were on universal credit and your parents helping you at times - it seems, at least at times, that you wouldn’t have been able to afford the service charge or maintenance costs. How many “ordinary middle class” parents are going to be buying their child a London flat and bankrolling the ongoing costs also. How does that fit in the “fairness” that is so important to you between yourself and your sibling?
You seem to have champagne tastes on a lemonade budget. This is not helped by all the people you know that were bought flats and had trust funds. Most people are mature enough to realise that some people are rich. That doesn’t make us or our family rich. “Whaa Bartholemew has a trust fund and bought a London flat and I want one too” is a pretty ridiculous look. No need for your parents to cash in all their assets and buy you a London flat in my opinion. In fact I think they would be foolish to do so when you can’t afford to run or maintain it and it would cause resentment with your sibling.
Perhaps once you get another job and can raise a mortgage your parents will consider lending you a 10% deposit (for a reasonable modest place) and changing their will to reflect this. They might have done this years ago if your requests were realistic.
Edited just to say I think when you are working you should look for a shared house of professionals. You sound like you would really enjoy that form of living. You could stay at your parents to save faster but that might be an uphill battle for your mental health.