Honestly, I don't need STO to influence me to rewatch any Star Trek series. I enjoyed them all. But in fairness to your post, I think STO influenced me to take another look at Enterprise as in all honesty, the decor of STO to me kind of feels most like that of Enterprise. Not quite sure why. Maybe it is that to me, STO feels unrefined and I felt Enterprise was unrefined. TNG was the complete opposite.
yeah I decided to rewatch them too. Though I am doing it in chronological order. started with new ST movie and finishing with voyager. I had never finished watchin Ent, ds9 or Voy, so it will be interesting. I actually enjoyed enterprise, minus the 3rd season. ds9 is a struggle, but I comitted to all of them so trying, lol.