The -i ending comes from Arabic which makes it seem a bit out of place in Myanmar (not to mention the obvious religious tension).
-ese, -ian, -an and -n all come from Latin via routes of varying directness, which is why they feel somewhat "neutral" in English (e.g. Congolese and Japanese both seem cromulent and not intrinsically African or Asian).
"Chinese" in English comes from Portuguese ("chinês"), who were some of the earliest Europeans there. -ês and -ese both come from the same Latin origin.
I hazard that words like Cantonese, etc., came either via the same route, or by back-formation to match the existing wider term "Chinese".
Interestingly, "Japanner" used to be another word for a Japanese person.