@Sqrtbottle, @snailboat Victor Mair has pointed out on numerous occasions how critically he views the current usage of the term 方言 in current Chinese and Japanese contexts, see for example
The point is that 方言 used to mean what he translates as 'topolect', a.k.a. 'regiolect', IOW "a language spoken in some place (other than here)". As such, the more classical use of 方言 is simply "a form of expression we need an explanation or even a translator for"; it is a very non-committal term.
In fact, what we call languages now have been historically sometimes been referred to as 方言, and this term also appears in the name of the office of translations of former Chinese dynasties.
By contrast, the modern idea of both the term 'dialect' and 方言 carry strong overtones of "a mere variant of the real thing", and this is (rightfully) what people from Hong Kong and Shanghai get P-offed by when the central government tries and suppresses the use of local idioms. It does so with the argument that these forms of expressions are not 'languages', they are merely 'variants of the one language', the implication being that they're faulty variants and therefore to be avoided and corrected.
To an extent, this may also be true for the situation in Japan. I cringe a bit when I read "Okinawan holds similar status in Japan; it's not mutually intelligible, but often seen as a dialect of Japanese because they have common ancestry, and are still politically united". First of all, which 'still' is this, the assertive one ('i still did it'—though it was frowned upon) or the temporal one ('i still did it'—when they saw me)? In case it's the latter: Okinawa is a very recent addition to the Japanese Empire (dating from the late 19th c,; read more on Tofugu).
Asserting that two forms of speech are "not mutually intelligible" and "are viewed as dialects" at the same time flies flat in the face of everything that 'dialect' wants to be as a term. The whole idea of 'dialect' in modern understanding is that "well they may sound peculiar but i can still talk to them". If it were to mean "i can't talk to them but we're of same origin so theirs is just a variant of my speech and X thousand years ago we would've sounded the same", well then, ultimately, all the languages of Europe, including Basque, are mere 'dialects' of each other, for it is thought that all languages derive from a single ancestor.
The whole idea of two languages having a common ancestor is also often somewhat overrated, as is the so-called 'genetic' ancestry of language. Languages mix and mingle quite freely, and Mandarin Chinese in particular is a language well known for having resulted from a melting pot of different peoples with different tongues.
What looks like a monolithic Japanese language is, likewise, the result of the coming together of a number of influences from different directions, not least because Japanese has taken over so many Chinese forms of expression and incorporated them so inextricably deep in the language proper. Sure you say "those are but loanwords!" but the fact is you don't say "ume (the plum) is not Japanese!" or "fude (the brush) is not Japanese" but you (like the Japanese themselves) only don't do that because you're not aware they're probably very old loans from Chinese. In other words, to some degree it so happens that something that we can trace the origin of we call a foreign influence, and something that we can not link to something somewhere else we call native. Tells you a lot about what we know, and sometimes little about the language at hand.