Why is Google not updating apps?

Add Your Google Account Again. There are chances that the Play Store is failing to authenticate your Google account and that’s why you aren’t able to update apps on your Android phone. You need to remove your current account from the device and add it again

I tried to install playstore update but it is not working. Google play won’t show up on the apps to be installed. Is there any way?

Try to reinstall google play store update. Install Google play instead. If it does not work, try to clear memory, remove unused files. Or if not, use another email that can be associated to your phone.