You ask a pretty simple question. The answer is also really simple. Yes, your amp is plenty good to power the speakers you are thinking of buying. Also, yes, you are likely to get a significant increase in sound quality and bring a big smile on your face.
Most of us, early on, got a pretty good sounding system that we enjoyed, and then for the rest of our life would upgrade one component at a time. Typically doing one at a time until reaching “the next level” and stay there enjoying it for a while (for me that is 5 - 7 years… but that varies between people).
So, the next step in your process replacing your speakers makes completely good sense. Then after they are broken in and you completely understand their sound… say 500 or more hours (which can easily be a year) you start considering what would be your next step. The listening to your new speakers will drive the decision on what next. If you feel you want more slam or dynamics, then the amp, if you want more natural sound or detail then maybe the preamp… or DAC.
Anyway, I think you are right on course.