I haven’t had that issue at all - actually the opposite, it’s been faster with response with the touch screen than my last phone
If it’s brand new , you have a 1 year warranty- why don’t you just take it to Apple and have them do a full check on it - and if it’s an issue you can get a warrant replacement
I got the 15 pro and I’m loving it - honestly one of my favorite iPhones , scratch that , one of my favorite phones I’ve ever owned
You shouldn’t be having any issues with the touch screen being unresponsive, not even partially. It shouldn’t be slow either
Whether it’s brand new or 2 years old you shouldn’t be having issues like that at all
Hope this issue gets worked out and you find a solution