Add duo_auto_mode UI toggle to Duo settings

What does this MR do?

This is the UI layer of Duo auto mode: it adds the frontend toggle and feature-flag plumbing so admins and group owners can control duo_auto_mode_availability. The underlying cascading setting and capability advertisement landed in Add duo_auto_mode cascading setting implementat... (!255441 - merged), now merged into master.

UI toggle

• Adds ee/app/assets/javascripts/ai/settings/components/duo_auto_mode_settings.vue, a new Vue toggle rendered on two pages: Group Settings > GitLab Duo and Admin Area > Settings > GitLab Duo.
• Wires the tri-state duo_auto_mode_availability value end to end through ai_common_settings_form.vue, ai_common_settings.vue, the settings pages, and index.js.
• Matches the cascading-lock behavior of the sibling tool_approval_for_session setting (same lock/inherit semantics at the group level).
• Pushes the duo_auto_mode frontend feature flag from the Duo configuration controllers, with the actor aligned to backend enforcement:
  • Admin: actor :instance.
  • Group settings: ee/groups_controller.rb and groups/settings/gitlab_duo/configuration_controller.rb use actor @group.root_ancestor.
• Admin::AiConfigurationPresenter exposes duo_auto_mode_availability only when the duo_auto_mode flag is enabled; when disabled, the key is omitted from the payload.
• Adds duo_auto_mode_enabled and duo_auto_mode_availability to the admin visible_attributes, plus the corresponding group settings helper wiring.

Feature flag

• Transitions duo_auto_mode from wip to beta: the definition file moves from config/feature_flags/wip/duo_auto_mode.yml to ee/config/feature_flags/beta/duo_auto_mode.yml, with type: beta and default_enabled: false.
• Done now because this MR completes the user-facing surface for the flag.
• Rollout is tracked in [FF] `duo_auto_mode` -- advertise the Duo auto ... (#629172).

Out of scope (lives elsewhere)

• The cascading duo_auto_mode_enabled setting itself, its columns/migrations, and capability advertisement (Ai::FlowsMetadataService, compute_server_capabilities) landed in Add duo_auto_mode cascading setting implementat... (!255441 - merged) (plus its split-1 migration MR), now merged into master.
• Governance relaxation for local surfaces (Ai::ToolRules::Permissions.local_effective, ResolutionService#local_surface?, read_only_files ask to allow) is part of the governance-surface re-key work, Auto mode: re-key GovernanceSurface + privilege... (#618761), which is stacked on top of this branch. None of that code is in this MR.

How to test

1. With the setting and flag present on master (from Add duo_auto_mode cascading setting implementat... (!255441 - merged)), enable the duo_auto_mode feature flag for the instance and/or group under test.
2. Confirm the duo_auto_mode_settings.vue toggle renders on both Group Settings > GitLab Duo and Admin Area > Settings > GitLab Duo.
3. Toggle duo_auto_mode_availability at the group level and confirm cascading-lock parity with tool_approval_for_session (lock state and inheritance from a parent group behave the same way).
4. Disable the duo_auto_mode feature flag, then confirm the toggle disappears from both pages and the admin payload from Admin::AiConfigurationPresenter omits duo_auto_mode_availability.

Notes

• Milestone: %19.5.
• Epic: [Auto Mode] Iteration 0: Client-side enabled au... (&23199 - closed).
• Spec coverage: duo_auto_mode_settings_spec.js, ai_common_settings_form_spec.js, ai_common_settings_spec.js, the Admin::AiConfigurationPresenter spec, the group settings helper spec, the admin Duo configuration request spec (asserts the pushed flag on/off and the presenter key gating), and the group settings request spec (ee/spec/requests/groups_controller_spec.rb, asserts the pushed flag on/off across the group hierarchy).
• Stack: the setting and flag landed in Add duo_auto_mode cascading setting implementat... (!255441 - merged) (merged into master); the governance re-key (Auto mode: re-key GovernanceSurface + privilege... (#618761)) is stacked on top of this branch.

Closes Auto mode: duo_auto_mode cascading setting, cap... (#618088 - closed)