How can benzaldehyde have a pKa of 14.9? There are numerous websites out there which claim that the pKa of benzaldehyde – C6H5CHO – is 14.90. (Just do a Google search for benzaldehyde pka to see what I mean.) This doesn't make sense chemically, as there are no protons in benzaldehyde which would be so acidic.

However, it doesn't seem to have been made up. The CRC Handbook of Chemistry and Physics lists the same value of 14.90 for the pKa of benzaldehyde, at $\pu{25 ^\circ C}$ in aqueous solution. But I can't find this information in the primary literature.

If this value refers to the acidity of the hydrate, does it include the equilibrium constant for hydrate formation? i.e. is this Ka the equilibrium constant for the reaction:

$$\ce{PhCHO + 2H2O &lt;=&gt; H3O+ + PhCH(OH)O-}$$

or is it just

$$\ce{PhCH(OH)2 + H2O &lt;=&gt; H3O+ + PhCH(OH)O-}?$$

I would appreciate some kind of definitive evidence. Using chemical reasoning and intuition is great, but if this value is to be of any use to anybody, then we need to know exactly what it describes.
Significant amount of geminal diol of benzaldehyde exists in an aqueous solution of benzaldehyde at 25 °C because $\mathrm{p}K_{\text{hyd}} = 2$ (Ref. 1)

The $\mathrm{p}K_{\mathrm a}$ of benzyl alcohol is listed as 15.40 (Wikipedia). Thus, one can reasonably assume that the given value of $\mathrm{p}K_{\mathrm a}$ 14.9 represents a composite equilibrium constant for the hydration of benzaldehyde and dissociation of the geminal diol thus formed.
Late addition to the answer:
In his paper, &quot;Acidity constants of benzimidazolium ketone and pyridinium aldehyde hydrates&quot; (Ref.2), Terence C. Owen states that:

It is known that the acidity constants of gem-diols typically are about 2.5 units lower than those of the corresponding monohydric alcohols.

When do some extensive literature survey, one can find few examples to backup that statement. For example, $\mathrm{p}K_{\mathrm a}$ of methanol is reported as 15.7 while that of formaldehyde hydrate is 13.3, between which $\Delta\mathrm{p}K_{\mathrm a} = 2.5$ (Ref.2). Interestingly, $\mathrm{p}K_{\mathrm a}$ of 1,1,1,3,3,3-hexafluoropropan-2-ol is reported as 9.22 while that of hexafluoroacetone hydrate is 6.45 where $\Delta\mathrm{p}K_{\mathrm a} = 2.77$ (Ref.3). However, $\mathrm{p}K_{\mathrm a}$ of 2,2,2-trifluoroethanol is reported as 12.37 (Ref.4) while that of 2,2,2-trifluoroethanal hydrate is 10.05 (Ref.3) where the difference is &lt; 2.5 ($\Delta\mathrm{p}K_{\mathrm a} = 2.33$).
Thus, we can conclude that the $\mathrm{p}K_{\mathrm a}$ of benzaldehyde is derived from its hydrate (gem-diol).
Also see: Yoshiro Ogata and Atsushi Kawasaki, In The Chemistry of Carbonyl
Group, Volume 2; Jacob Zabicky, Ed.; John Wiley &amp; Sons Ltd.: New York, NY, 1970, Chapter 1: Equilibrium additions to carbonyl compounds, pp 1–69 (https://doi.org/10.1002/9780470771228.ch1).

Late Edit:
It is also noteworthy that $\mathrm{p}K_{\mathrm a1}$ of the cyclic hydrate of hthalaldehyde is reported to be $11.50 \pm 0.10$ at $\pu{25 ^\circ C}$ (Ref. 5):