Is it normal that despite me buying a game on sale for the maximum amount possible, now that the full price has increased I can't access the latest version anymore. Like, is it something that happens to all games on itch.io?

No, that's not normal, but it's possible if the developer sets a minimum price on the files.

There are two ways to set prices on itch: the price on the game and the price on the individual files.  Normally, the developer sets the price for the whole game.  If you buy the whole game, you own it forever, regardless of what you paid for it.

The price on individual files is intended as a way for the developer to offer bonus materials to customers who pay more than the normal price for a game.  You can only download those files if you paid at least that much for the game.