Render sign in form with Vue

What does this MR do and why?

Related to #574982

We want to migrate the sign in form to Vue so it gives us more flexibility for Organization/cells sign in. Specifically we will be moving to a two-step sign in flow where you first enter your email/username and then dynamically show the password field after an API call. See https://gitlab.com/gitlab-com/content-sites/handbook/-/blob/9d937082be9fa7dc03ded91e7510ee3c3e2eef13/content/handbook/engineering/architecture/design-documents/organization/decisions/007_organization_sign_in.md for the proposed sign in flow for Organizations/cells

See TODO section in the issue for TODOs that need to be completed after this MR is merged.

References

• gitlab-com/content-sites/handbook!17071
• https://gitlab.com/gitlab-com/content-sites/handbook/-/blob/9d937082be9fa7dc03ded91e7510ee3c3e2eef13/content/handbook/engineering/architecture/design-documents/organization/decisions/007_organization_sign_in.md

Screenshots or screen recordings

Before	After

With captcha enabled

Before	After

Before	After

Unconfirmed user

Before	After

SAML

Screen_Recording_2025-12-02_at_4.34.40_PM

OmniAuth (Google)

Screen_Recording_2025-12-02_at_4.17.20_PM

Passkeys

Screen_Recording_2025-12-02_at_4.18.24_PM

LDAP

Screen_Recording_2025-12-02_at_4.45.56_PM

Regular sign in with LDAP enabled

Screen_Recording_2025-12-02_at_4.47.06_PM

How to set up and validate locally

1. Go to /rails/features and enable sign_in_form_vue feature flag
2. Sign out
3. Sign in

Recaptcha

See https://docs.gitlab.com/integration/recaptcha/

Unconfirmed users

See https://docs.gitlab.com/security/user_email_confirmation/

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.