If you meant that you want to set the current user as the default value for SharePoint person or group column, then I think this cannot be achieved in PowerApps. If my understanding is incorrect, please feel free to let me know.
Per my certain knowledge, when an Edit form control is in New mode, the Item property is ignored. The form doesn't show an existing record; instead, the values in each field match the default values of the data source with which you configured the form.
So though you can set the current user as a Default user using User() in People picker field, the value in this field does not match the default values of the data source. So if you don’t click on the People picker control before saving the data, the data cannot be saved to data source, and you are asked to enter a required value to the required field.
For People picker field, on Edit screen, you need to search a user by entering user name, then select one from drop down items.