Why can’t I change my time zone manually?

There is your answer. You have screen time blocking you from changing your time zone. Here is the support article if you have forgot your passcode. You should be able to choose "Change Screen Time Passcode", then after choosing Forgot Passcode, entering your Apple ID Password should let you reset it. More information can be found in this Support Article.

If you forgot your Screen Time passcode - Apple Support

If your Apple ID has changed since the passcode was set up you will need to Contact Apple Support using the link provided in that Support Article.

The reason is shown in your screenshot.

”The time zone can not be set manually due to device restrictions.”

We cannot guess why your device is restricted, but you likely know.

There are restrictions in place in your Screen Time settings that are preventing you from changing the setting. Turn off Content & Privacy Restrictions in Screen Time > Content & Privacy.

Mac Jim ID likely explained.

If not, perhaps your iPhone is managed by an employer or educational institution.