test(e2e): ensure advanced types work in forms also

test/e2e/cypress/integration/profiles/email/login/error.spec.ts

@@ -49,9 +49,13 @@ describe('Basic email profile with failing login flows', () => {
 
         it('should show an error when the identifier is missing', () => {
           cy.submitPasswordForm()
-          cy.get('*[data-testid="ui/message/4000001"]').should(
+          cy.get('*[data-testid="ui/message/4000002"]').should(
             'contain.text',
-            'length must be >= 1, but got 0'
+            'Property password_identifier is missing'
+          )
+          cy.get('*[data-testid="ui/message/4000002"]').should(
+            'contain.text',
+            'Property password is missing'
           )
         })
 

test/e2e/cypress/integration/profiles/email/registration/success.spec.ts

@@ -58,7 +58,8 @@ context('Registration success with email profile', () => {
         cy.get('input[name="traits"]').should('not.exist')
         cy.get('input[name="traits.email"]').type(email)
         cy.get('input[name="password"]').type(password)
-        cy.get('input[name="website"]').type('')
+        const website = 'https://www.ory.sh/'
+        cy.get('input[name="traits.website"]').type(website)
 
         cy.submitPasswordForm()
         cy.get('pre').should('contain.text', email)
@@ -69,9 +70,9 @@ context('Registration success with email profile', () => {
           expect(identity.verifiable_addresses).to.be.undefined
           expect(identity.schema_id).to.equal('default')
           expect(identity.schema_url).to.equal(`${APP_URL}/schemas/default`)
-          expect(identity.traits.website).to.equal('')
+          expect(identity.traits.website).to.equal(website)
           expect(identity.traits.email).to.equal(email)
-          expect(identity.traits.age).to.equal(0)
+          expect(identity.traits.age).to.be.undefined
           expect(identity.traits.tos).to.equal(false)
         })
       })