What satellite catalog contains the absolute magnitude of the most number of stars?

Hi, Not sure why you need this data (if we know, we can help better!) but once you have the distance (i.e., parallax, from Gaia) and the apparent magnitude, also from Gaia you can just set up a spreadsheet to calculate the absolute magnitude. Formulae for doing that (I cant recall it accurately off the top of my head) can be found all over the internet.

Just a note: visual magnitudes in Gaia are from the V filter, which is similar to, but not exactly the same as, v (i.e., the 'eye' magnitude).

As Mike said, Gaia (EDR3, with DR3 due for June) is the most complete source of information.
I do not tend to follow the absolute magnitudes published in those catalogues though, but to get values calculated using their parallaxes and derived magnitudes.
Always have to keep in mind that the further away an object is (smallest parallax), the errors in those values will be too large for a useful determination. Just to give you an example, a lot of QSOs would be placed in the Milky Way if we were to trust those results at face value...
Also, stars surrounded by nebulae may have spurious parallaxes and thus wrong absolute magnitudes published.

Finally, Gaia does not have a V filter, it uses a broad band filter which gives magnitudes (the so-called G band mags) similar to Sloan's r for normal stars (not too red or too blue) and two spectrophotometers which provide BP (blue) and RP (red) magnitudes. We can derive a rather good V mag. from those using transformations (but again, not for too red stars).

Cheers,
Sebastian