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I have tried to figure this out, but cannot find an answer anywhere...

Are, perhaps, astronomers unsure of its exact spectral class? (I have heard that red dwarfs are usually variable... to an extent...)

Books and articles talk about M0 stars, M0V, and M4, but not M4.0V...

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It's M4V, not M0V.

In principle, spectral classes can be further subdivided, particularly in the M class, because there are significant differences between an M4 and an M5 spectrum for instance.

Therefore you may see spectral classifications of M4.0 or M4.5 for instance (and even finer subdivisions are occasionally quoted).

The difference between M4 and M4.0 is the implication that the spectral class has been determined more precisely for the latter.

The V just means it is a dwarf. This can also be judged from the spectrum and is therefore part of a full spectral classification.

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