What is the degree of ionization is the solar photosphere?
The degree of ionization in the photosphere varies with depth of course, but overall it is small.   Table 1 of the Bilderberg Continuum Atmosphere  (Solar Physics, 3, 5, 1968) gives the pressure and the electron pressure at various optical depths in a comprehensive model.  The ratio of the pressure gives the Ne/Ntotal.  At optical depth = 1 at 5000 Angstroms, Pgas = 1.412E5 (cgs) and Pe = 6.239E1.  The ratio is 4.4E-4. The hydrogen ionization, also given in the table is 4.07E-4.  The model assumes Helium abundance of 0.1 which is off a bit from the modern number of 0.087.