Unship: Next badge from global topbar
### Problem to solve
The navigation sidebar is a dense region and each element should be thoughtfully evaluated. The `Next` [badge was added in 11.1](https://gitlab.com/gitlab-org/gitlab-foss/-/issues/46048) and is given prominent, persistent positioning — but its marginal information value is low and it creates several UX issues:
1. **Confusing user journey** — Users must navigate to a separate site (next.gitlab.com) to toggle GitLab Next on/off, then return and refresh to see the badge change state.
2. **Unclear purpose** — The badge is primarily an infrastructure tool, not a user-facing feature. Most users encountering it have no context for what it means.
3. **Limited value** — Users on Next are opt-in; they don't need a persistent reminder on every page load that they are on the environment they explicitly chose.
4. **Precious real estate** — The navigation chrome has limited space that could be better utilized.
Additionally, the badge's role as a verification signal is largely redundant:
- **The favicon already carries the canary signal.** When a user is on canary, the browser tab displays a yellow tanuki, which is visible in every screenshot attached to a bug report or support ticket and is sufficient for both self-verification and triage.
- The badge is mostly a convenience for our Infrastructure team, but the favicon provides an equivalent (and arguably better, because screenshot-friendly) signal for the same workflows.
<details>
<summary>Background</summary>
Users that have opted in or those visiting an area within [gitlab-org](https://gitlab.com/gitlab-org) or [gitlab-com](https://gitlab.com/gitlab-com) will be using our canary infrastructure, which means they will see the latest version of GitLab a few hours before it lands in production.
To opt-in users must first open their menu and select `Switch to GitLab Next`

This will open a new tab ( next.gitlab.com ), then user must adjust the toggle
{width="440" height="300"}
Once they return to GitLab and refresh the page the `Next` badge will appear.

> #### Confirming I am using the "canary" stage of an environment [**_#_**](https://handbook.gitlab.com/handbook/engineering/infrastructure/environments/canary-stage/#confirming-i-am-using-the-canary-stage-of-an-environment)
>
> The best method when using the UI is to [enable the performance bar](https://docs.gitlab.com/ee/administration/monitoring/performance/performance_bar.html) and look at the name of the Kubernetes pod service your page. If it starts with `gitlab-cny` (and has a baby chicken next to it), you are using the canary stage. There will also be the word "next" in a green box next to the GitLab logo in the top left.
{width="414" height="140"}
**Fav icon differences**
| Default | Canary |
|---------|--------|
|  |  |
</details>
### Proposal
Remove the `Next` badge from the navigation. Users can continue to toggle GitLab Next within the user menu, and canary state remains visible via the yellow tanuki favicon (screenshot-friendly for triage) and the performance bar (`gitlab-cny` pod prefix).

### Benefits
- **Cleaner UI** — Reduces visual clutter in the global navigation
- **Better space utilization** — Frees up valuable navigation real estate for more relevant user features
- **Reduced confusion** — Eliminates an infrastructure-focused indicator from the user interface
- **Simplified experience** — Users who need GitLab Next can still access it through the user menu without the persistent badge
### Alternative considerations
If visibility into GitLab Next status is deemed necessary beyond the favicon:
1. **User settings indicator** — Show status only in user preferences/settings where users manage the toggle
2. **Contextual notification** — Display a one-time notification when GitLab Next is enabled, rather than a persistent badge
3. **Admin-only visibility** — Limit the badge to group owners or admins who manage GitLab Next enrollment
### Implementation notes
- Verify no dependencies on the badge for user workflows
- Consider analytics on badge interaction to validate low engagement
- Ensure GitLab Next toggle remains accessible in the user menu
- Update the [canary stage handbook page](https://handbook.gitlab.com/handbook/engineering/infrastructure/environments/canary-stage/) (tracked in child task https://gitlab.com/gitlab-org/gitlab/-/work_items/601954)
### Target audience
- GitLab SaaS users (all tiers)
- Product and UX teams focused on navigation simplification
### Related
- Consolidates duplicate https://gitlab.com/gitlab-org/gitlab/-/work_items/581062 (closed in favor of this issue)
issue