Browsing in not a problem unless you are within close range of another person who is also browsing. Looking at clothes in a supermarket is no different than browsing for say cheese, and Ive come across a lot of people who spend a lot of time browsing for fresh food.
As for the virus staying on things for a while, yes it can and always has, which is why hand hygiene is so important, And today supermarkets are so much better than last March in supplying sanitiser for the customers.