Migrate "New group" form to Vue

Background

Currently the "New group" form (https://gitlab.com/groups/new#create-group-pane) is a mixture of Vue/HAML/jQuery. We are in the process of building the form out in Vue for Organizations in #410804 (closed). Once that is complete we should use that Vue form for the main "New group" form to reduce technical debt and have a consistent UX experience across all of GitLab.

Proposal

Use the Vue from build in #410804 (closed) to migrate the from on https://gitlab.com/groups/new#create-group-pane

Implementation guide

1. Create a new_group_app.vue file in app/assets/javascripts/groups/components
2. Render app/assets/javascripts/groups/components/new_edit_group_form.vue
3. Move the newSubgroup logic in app/assets/javascripts/groups/components/group_name_and_path.vue#L314 into app/assets/javascripts/groups/components/new_group_form.vue
4. Add hidden inputs in new_group_app.vue that update with the values from app/assets/javascripts/groups/components/new_group_form.vue.
5. Mount form in app/views/groups/_new_group_fields.html.haml
6. Update feature specs and QA E2E tests