Here is a great game, it's not a multiplayer ttrpg, but still in the spirit of writing letters: Quill, by Scott Malthouse https://trollish-delver-games.itch.io/quill-a-letter-writing !
I can also recommand you to look at solo TTRPGs here : https://itch.io/c/574927/the-hermit-club-list-of-all-solo-ttrpg-and-larp-on-itch... → a lot of them are writing games (for example writing a diary or writing a letter being lost in space) and I guess it can give ideas/mechanics to create an epistolary game :)
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You also got epistolary games like:
- Sincerely https://www.drivethrurpg.com/product/206314/Sincerely about being 2 women in love, during the 19th century: so you have to hide your secret love - I find this idea really nice, and you can easily play keeping the same idea but with a different secret
- or Worlds of Ruin https://ideomotoring.itch.io/worlds-of-ruin in a dark fantasy world
- or Reverie Cycle https://seaexcursion.itch.io/reverie-cycle which is more poetic
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To begin or to get ideas, you can be inspired by writing exercises ( http://writingexercises.co.uk/index.php )