Question for people with H1B visa in the US who have global entry?

I recently got my global entry application approved after the biometric appointment… Yay! If you are an H1B visa holder and have a global entry card :- 1. Do you have to get a new H1B visa stamp that matches your new approved H1B petition in order to use global entry? Or like always can you continue with the old H1B visa stamp that is valid and use the new approved H1B petition to reenter the US? 2. How often do you go to the global entry office to update your immigration information? TC - 160k