After knowing that low pressure sodium lamps emit a monochromatic yellow light with a CRI of 0 and high pressure sodium lamps emit a yellow light that renders some colors with a CRI of 22, if medium pressure sodium lamps were to exist, what would be their CRI and what degree of yellow light would such lamps produce?

The high pressure are in fact the broadened D line, minus the D line alone getting absorbed.
So when lowering the loading, the broadening is just not as wide and less amount of colder sodium (responsible for the absorbtion), so some of that remains. So really just something between the HPS and LPS light.
But it would not be of any practical use: Worse light color than HPS and less efficient.

How would medium pressure sodium lamps become less efficient than high pressure sodium lamps even though low pressure sodium lamps are much more efficient than high pressure sodium lamps?

I mean definitely less efficient than low pressure, but with color nearly as bad as the low pressure.
And then  it is the question how the tube would really be designed.
The low pressure were designed as low pressure because at that time there were no materials capable to withstand the loading of any higher pressure discharge (and the chemical reactivity of the sodium with the glass available that time).

The capability to process PCA was, what allowed the higher temperatures of the HPS, so the design goal was to get as much as possible from that, mainly in term of the compact light source size (to improve the optical efficiency of fixtures) and color quality. Making "something between" just did not make any commercial sense, as it would require the use of PCA witrh larger size (quite expensive material, compare to glass; it is only cheaper in lamps because of the way smaller amount of it in HPS compare to the glass in LPS).
So such lamp would have efficacy about comparable to HPS, color quality of LPS (dominant would be monochromatic), no benefit of monochromatic light in fogs (as there would be some broadening, causing the unwanted scatter; the motivations why LPS were specified) and expensive construction because the need of large PCA arctube.