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thats kind of confusing and sorry if this doesn't help but maybe this one?
http://www.mangago.zone/read-manga/kanawanu_koi_no_musubikata/
it does involve red string but they werent fated and fell in love either way
But can’t remember what it was called there was a way for two people to know they were true lovers I don’t remember how but there was a way to know it (not the red string) and the two main characters fell in love with eachother but they weren’t fated lovers but they stayed together regardless even tho one of them was always scared the other should be with their fated lover, i don’t remember what happend after but yeah that’s it plz help ♂