The solar neutrino luminosity is about 2.3% of its electromagnetic luminosity (i.e. light). So the extra mass lost in the form of neutrino energy is 2.3% of your original calculation.
The average mass loss in the form of a wind and coronal mass ejections is about $4\times 10^{16}$ kg/year, but varies with the solar cycle (and from cycle to cycle) (Mishra et al. 2019).
4.5 billion years ago? It depends how exact you want to be. The Sun is thought to be 4.57 billion years old, so 4.5 billion years ago it would have been 70 million years old.
A 70 million year old Sun would have been on the hydrogen burning main sequence and about 20% less luminous than it is now, so you can scale your luminosity-mass and neutrino mass loss rates by about 0.8.
However, the solar wind was probably much stronger than it is now. The observational constraints on this are weak, but theoretical models suggest the mass loss rate in the wind scales as rotation rate $\Omega^{1.33}$ (Johnstone et al. 2015). Unfortunately, we still don't know how fast the Sun rotated in its infancy; it could have been anything from about 10 to 100 times it's rotation rate now. That means the mass loss rate in the wind would have been 20-500 times what it is now. Thus mass loss from a wind would dominate.
But maybe you meant $\sim 4.5$ billion years ago, in the sense that you wanted an answer for before the Sun became a star. i.e. Before hydrogen fusion began at a few million years after the Sun's birth. In that case, the wind losses might have been as per the 70 million year old case (with similar uncertainties), but there would be no neutrino losses (no nuclear reactions) and the luminosity of the Sun could have been a factor of 10 higher as a contracting pre main sequence star. In that case, mass loss from a wind would probably still be the biggest contributor.
