Use proper vue frontend errors on company form

What does this MR do and why?

Use proper vue frontend errors on company form

• use proper vue way with gl form fields

• fix error submission field remembering

• implement dropdown changes for Improve the country/state selector to use listb... (#549546 - closed) on this form

• see https://gitlab.com/gitlab-org/gitlab/-/issues/542126

Changelog: other EE: true

Screenshots or screen recordings

item	Before	After
/users/sign_up/company/new	no change
country dropdown
state dropdown
validation video	Screen_Recording_2025-07-02_at_4.47.36_PM	Screen_Recording_2025-07-11_at_2.16.04_PM

How to set up and validate locally

1. Setup to simulate SaaS and restart GDK
   • Make sure Admin > Settings > General > Sign Up Restrictions match the below (no admin approval, but hard email confirmation)
2. visit /-/trial_registrations/new on your gdk site.
3. Register
4. Confirm email by finding the confirmation path from last User created in rails console
   • Rails.application.routes.url_helpers.user_confirmation_path(confirmation_token: User.last.confirmation_token)
5. Visit that Url
6. Sign back in when directed.
7. Fill in the welcome form with My company or team and submit.
8. At this point you should see the differences shown in the before/after screenshots

MR acceptance checklist

Evaluate this MR against the MR acceptance checklist. It helps you analyze changes to reduce risks in quality, performance, reliability, security, and maintainability.

Related to #542126 (closed)