Can’t change phone time - set automatic time grayed out
There are a few reasons as to why this might be disabled.


Do you have an Exchange account connected to the phone? There might be a policy connected to it, disabling the option to change the timezone.
If you look in Settings > Privacy > Location Services > System Services (in the bottom), is the option "Setting Time Zone" disabled?
If you have Screen Time enabled with a pass code, that might also disable the option to change time zone. Try to disable Screen Time, restart, and then try again.


Hope that solves it for you.