Formula fields and buttons can only be displayed on the form in two cases:
When editing a record (not creating a new one).
When creating a record with Compute Mode enabled.
Formula fields are supported in the form. Doing live calculations inside the form is possible by enabling Compute Mode. You can find the option in the advanced section on the settings page.
Button fields in Airtable are in fact formulas. The only way to show them in the form is after a record is created. Because of that, they can only be shown when a form is either editing a record or Compute Mode is enabled.
In the portal, you see records that already exist in Airtable, therefore the buttons are shown there. The same is not true when’s form is being used and no record exists yet in Airtable.