Ok, Imma make this quick, the first letter is from hoid, no questions there, but i believe he is sending similar copies of the letter to the entire 16 shards, and frost.
Frost’s reply is the second letter, with his non-intervention policy.
I think that the third letter, (1st one found in oathbringer) is Ati’s response, remarking how nobles are fooled by people acting as beggars (you know. Like hoid did in mistborn) and how hostile the recipient is to Hoid, additionally, like Leras, he refers to hoid as Cephandrius.
I think the fourth letter is written by leras, saying that “I am surprised you found us, WE hid this place well.” (Meaning how preservation and ruin built scadrial as the only planet in the habitle zone)
I also think that the 5th letter is written by Harmony, completing the scadrial trilogy. Which is why he is new to godhood, and inquiring about Adonalsium and who hoid is.