https://en.wikipedia.org/wiki/E_language
It appears to be a Tai Chinese creole or mixed language (like a creole but without the massive simplification in grammar).
Yi(Loloish) is definitely a different language family though that wouldn’t stop people writing in Mandarin if they really wanted to. Vietnamese, Korean and Japanese were all written as if they were Classical Chinese to greater or lesser extents until relatively recently.
https://en.wikipedia.org/wiki/Loloish_languages
I’ve heard Sichuanese described as Mandarin without tones. All of Sìchuān speaks different forms of Mandarin for the same reason Manchurians do, recent massive resettlement, though not as recent as in 东北.
If Sichuanese sounds similar to Mandarin due to migration, it would certainly explain a lot. Thanks for that bit of information. But I would say that the differences between Sichuanese and standard Mandarin would be more from pronunciation differences than tonal differences.
https://en.wikipedia.org/wiki/Nuosu_language
> Nuosu is one of several often mutually unintelligible varieties known as Yi, Lolo, Moso, or Noso; the six Yi languages recognized by the Chinese government hold only 25% to 50% of their vocabulary in common. They share a common traditional writing system, though this is used for shamanism rather than daily accounting.
I bow to your superior expertise when it comes to the differences between Sichuanese and Mandarin but all of Sìchuān is definitely part of the Mandarin speaking area.
The book to buy if you’re interested in this is the Language Atlas of China.