beginner question - how much does tire profile/grip affect lean angle?

I'm only on my 4th track day (middle aged dude trying to relive my youth) and trying to better my corner speed. Per my mentor/instructor, I'm doing a good job with racing lines, bp, throttle control, but yet to learn trail braking and other advanced shit.I'm on a '16 street triple and my first set of tires are do for a replacement. I have Michelin Power RS right now. I chose them because they heat up faster for daily street riding and I've always liked how the initial turn in feel on them is (I have on my duke 390 as well after replacing the rosso 2).so my question, what tire should I go with for the next 2-3 track sessions?Does choosing the wrong tires hold back progress at all? Or is this all mental and I have not reached the level to even feel the difference?And I side question: what kind of progress can I expect on triumph street triple (detuned daytona) ? I know I'm not even close to hitting the limits of the bike, but I also hear comments about not hitting hard parts and should I hang off the bike more if I am hitting pegs/toes. But then I watch my mentor and leaders and they lean way more than I think the striple is capable of since I'm already scraping pegs. via /r/Trackdays https://www.reddit.com/r/Trackdays/comments/cu8a2w/beginner_question_how_much_does_tire_profilegrip/?utm_source=ifttt