How would one precisely use ‘Chinese’ without qualifiers and where ‘Sino’, ‘Cantonese’, ‘Mandarin’, etc. is not applicable?

If you start from the premise that Chinese is a language and that Mandarin and Cantonese are Chinese dialects, then a good question might be:

What Chinese dialect do you speak? (A: Cantonese, Mandarin).

I have never heard of a language described Mainland Chinese as it would be almost meaningless. (Two "Mainland Chinese" speakers could read and understand the same written article, but depending on where said speakers are from, they may or may not speak mutually intelligible dialects.)

To your question:

Is there a situation where I can use the word 'Chinese' without qualifiers and where other words are not actually more precise...

Yes: Do you want to order Chinese take-out?

And removing tongue from cheek, a decent question (and accepted answer) are at a sister website, Chinese Language.