acid base - Is methanol really more acidic than water?

The question Why is methanol more acidic than water? deals with the reasoning of why methanol is more acidic than water. However, as mentioned in the comments of that question, the acidity constant of water is $14.0$, as confirmed by two sources$^{[1][2]}$, with one of them offering a very convincing explanation. The Wikipedia page$^{[3]}$ for methanol quotes its acidity constant to be $15.5$.

So it would seem, water is more acidic than methanol. But an answer to the question mentioned above gives a good reasoning for why methanol is more acidic than water (it doesn't deal with the pKa of water, though). Also, the answer mentions that water would be much worse an acid in DMSO. Another question implies that methanol and other alcohols are more acidic than water.

On the other hand, it is also true that we regard alkoxide ions as being more strongly basic than the hydroxide ion (thus we use them primarily for elimination reactions).

This leaves us in a fix. So what is the ultimate truth?

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<sub>[1]: What is pKa of water? - Chemistry ChemLibreTexts
[2]: Water (Data Page)

[3]: Methanol</sub>

Answer

First, water's $\ce{pK_a}$ in water is $\ce{14}$ as explained here. This means that $\ce{H2O}$ is slightly dissociated in liquid form, such that $\ce{[H+] = [HO-] = 10^{-7}}$.

Second, I would say that caring too much about which compound is the best acid is a bit like arguing by definition. Acidity is a fuzzy concept used as a shorthand for deeper meaning. This means there is little point arguing about the shorthand when we have the actual properties it synthesizes.

In this case (sou rce):

$$\begin{array} {|c|c|c|l|} \hline \ce{solvent} & \ce{pK_a\ of\ water} & \ce{pK_a\ of\ methanol} & \ce{Interpretation} \\ \hline \ce{water} & 14.0 & 15.5 & \ce{water\ is\ more\ dissociated\ than\ methanol} \\ \hline \ce{DMSO} & 31.4 & 29.0 & \ce{methanol\ is\ more\ dissociated\ than\ water}\\ \hline \end{array}$$ So you can argue (as in the answer you linked) that methanol is more acidic than water in the abstract sense, because $\ce{DMSO}$ doesn't stabilize the anions by hydrogen bonding and so is closer to the "ideal" case (whatever that may be).

But what's the point ? You already have the $\ce{pK_a}$ values, any practical question you might have about the concentrations of theses solutes in $\ce{H2O}$ and $\ce{DMSO}$ is already answerable.