Hook up new organization group form to API

What does this MR do and why?

Related to #410804 (closed)

The grouptenant scale team is starting to build out an Organization MVC. For more information about what an "Organization" will be see https://docs.gitlab.com/ee/architecture/blueprints/organization/

This MR builds on top of !142598 (merged), !143709 (merged), !144425 (merged) and !145326 (merged) to continue building out the form to add a group to an organization. This MR hooks the form up to the POST /groups API so a group is actually created when submitting the form.

Reviewer notes

1. Future MRs will add:
   • Your group name must not contain a period if you intend to use SCIM integration, as it can lead to errors. alert that is shown on https://gitlab.com/groups/new#create-group-pane
   • Add Who will be able to see this group? View the documentation under Visibility level label. We need to add support upstream in gitlab-ui!3982 (merged) before this is possible.
2. The plan is to use this new Vue form to refactor /groups/new#create-group-pane (#440464) and /admin/groups/new ( #440466) to Vue in the future.

MR acceptance checklist

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Screenshots or screen recordings

Screen_Recording_2024-02-28_at_12.21.06_PM

How to set up and validate locally

1. Enable the feature flag
   • echo "Feature.enable(:ui_for_organizations)" | gdk rails c
2. Navigate to /-/organizations/default/groups_and_projects
3. Click New group
4. Fill out the form and click Create group
5. Navigate back to /-/organizations/default/groups_and_projects. The newly created group should be there.