I read your comment three times, but you write without point nor comma in one go and make no pause and it is hard to read and to understand what you are even talking about and I understood that you complain most about the changing of the ordering of games.
Projects dissappear from time to time, so the ordering will always change sometimes at the page border, no matter what you do. Or they might have their tags changed.
And projects can get a bump on the recent sorting for having a devlog with a major update.
There are more filters in the directory. https://itch.io/directory
The year filter in combination with tags might be of interest to you.
It sounds to me like you want to tackle a few thousand games in a tag selection and want to keep track what you have already seen and what not. On desktop browser I could offer you a tool for that. If you are willing to manipulate the url you could use page numbering, even in endless scroll. But that sounds like a hassle on mobile. You can enter a number manually in "?page=11". The max page should be around x/36 where x is the number your browser shows as the game counter. The lack of a back button is not helping there, and going backwards on the popular sort is not actual a good idea anyway.
But you can go backwards on the recent sort. Exchange newest with oldest in the url.