'Anyway' is not folksy, whatever that means, it's just a regular word. 'Anyways' is an American word. I have however noted recently that one or two younger British people have used it when I've spoken to them (younger meaning less than 30.) American media is everywhere in the UK, no doubt this trend will continue to grow. But no, by and large, at present 'anyways' is not used in BrE.

Anyway is a standard English word - not folksy. Anyways is non-standard, and is commonly used in the US and Canada. Anyways is more colloquial and 'folksy'.

Folksy? I'd say "anyway" is a bit informal, possibly a bit colloquial, but it's a word I see all the time. "Anyways" is even more colloquial, but still not "folksy" in my experience. I don't speak very much to British English speakers so I can't comment on if they use it or not. In more formal situations people tend to use words and phrases such as "furthermore," "that aside," and "moving on..."

Thank you for your answers. Now it's clear for me that "anyway" is a standard word, but "anyways" is colloquial and not used in British English.

I'm not sure what they mean by "folksy". Everybody uses it in everyday speech. Yes, it's colloquial in the sense that you usually won't see it in formal writing. I can't comment on the British English part.