What proportion of the energy input to the ocean tide system comes from the sun?
From [1, 2], the oceans are dissipating about 3.5 TW of energy. The moon and sun input about 3.2 TW and 0.5 TW, respectively. (0.2 TW of the 3.7 TW are dissipated by the solid Earth and the atmosphere.) Another estimate of tidal energy dissipation [3], looking at the 8 major tidal constituents, estimates 0.411 TW of solar tides dissipated by the ocean. (With an additional 0.03 TW dissipated by a moon-sun interaction constituent.)   

[1]: Munk and Wunsch, 1998, https://doi.org/10.1016/S0967-0637(98)00070-3

[2]: Jayne and Laurent, 2001, https://doi.org/10.1029/2000GL012044

[3]: Egbert and Ray, 2003, https://doi.org/10.1029/2003GL017676