In next-gen project, the fields created are specific to that project.
So, I assume you want to make the fields as mandatory/required for a Classic project.
You can create a new field configuration and use it in your project so that it'll not affect other projects. You mark the fields as required in it.
I typically prefer to make the field required associated with a specific transition, e.g. the Create. This is done by editing the workflow and adding a Validator to the transition(s) where you wish the have the field updated.
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