> I’m pretty sure there remains a discrepancy between the predicted mass of the Higgs boson and the measured mass in experiments. Is this resolved then?
Sort of.
The higgs boson mass is a parameter to the Standard Model. As far as the Standard Model is concerned, that is the end of the story. There are just a series of constants need to be fitted to data in the Standard Model and that's one of them.
However, the "problem" is why ~125GeV. If there are extremely high energy particles (which are expected in a Grand Unified Theory), then corrections to the Higgs mass would be enormous. This is a fine tuning problem where we arbitrarily tweak those corrections such that we magically end up at 125GeV. Supersymmetry and other Beyond Standard Models look to 'fix' this, and that's where my knowledge ends.
Honestly, when I was doing my PhD I took the pragmatic view on this. Trying to infer things at energy scales we can't probe struck me as more as a mathematical exercise than Physics. Many, many people would disagree with that though (and staked their careers on it).