[Arrow] Integrate `ExtensionType::validate` within `ExtensionType::try_new`

[sdf-jkl]

Is your feature request related to a problem or challenge? Please describe what you are trying to do.

In #9677 @scovich and @alamb proposed integrating the new validate API within try_new.

It will reduce code duplication, improve modularity and prevent the potential slowdown from using the default value.

Describe the solution you'd like

Move the ExtensionType validation logic from the try_new into validate. Use validate in try_new.

Describe alternatives you've considered

Not do anything since there aren't too many plain validation cases in the codebase yet.

Additional context