> Even my sorry laowai Chinese can make some of it out

In a similar way, as a not-great Spanish/French speaker, I can understand lots of Italian words and grammatical constructions, and often get the gist of random Italian quotations that pop up in books written in English.

Doesn’t make them the same language.

You are seriously overestimating how much Chengdu hua or Kunming hua differ from mandarin. Yes, they are crazy weird accents, but no, it’s not like a Spanish speaker picking out some Italian words, not even close. Same goes for dongbei hua or shandong hua, it only starts getting weird in south east China (Cantonese, fujian/min yu, kejia hua, etc...), and even then, those dialects are still Chinese with lots of nuances, not to mention they are similar to each other as well.

According to Wikipedia, Sichuanese shares <50% of its vocabulary with Beijing Mandarin. That is significantly further apart than French or Spanish to Italian. (Disclaimer: I know very little about the relation between Sichuanese and Beijing Mandarin, and would be happy to see better explained quantitative comparisons.)

Maybe you are underestimating how close Romance languages are.

In any event, I think everyone would agree that Sichuanese is much closer to Beijing Mandarin than other Chinese languages (like Xiang, Wu, Hakka, Min, etc. etc.).

Link?

Here: https://en.wikipedia.org/wiki/Varieties_of_Chinese

Officially sichuanese isn’t even considered another variety of Chinese (nor are any other western Chinese dialects). It’s even just called southwest mandarin: https://en.wikipedia.org/wiki/Southwestern_Mandarin

The page specifically for chengdu mandarin doesn’t mention anything about 50%...https://en.wikipedia.org/wiki/Chengdu-Chongqing_dialect