Gracefully transition from old cookie to new cookie

Description

Gracefully transition from old cookie to new cookie.

Context - !34 (comment 2654157571)

Screen Recording

Screen_Recording_2025-07-29_at_11.55.58_AM

Steps to verify

1. Ensure you are using GitLab Workspaces Proxy on 0.18 container tag. If you are not sure, run scripts/remote_development/workspaces_kubernetes_setup.sh from the GitLab folder.
2. Create a new workspace and open it up. Verify the cookie domain is a wildcard(starting with .).
3. Patch the image of your GitLab Workspaces Proxy to running kubectl -n gitlab-workspaces set image deployment/gitlab-workspaces-proxy gitlab-workspaces-proxy=registry.gitlab.com/gitlab-org/workspaces/gitlab-workspaces-proxy:dev-20250729062318
4. Refresh the workspace and confirm the cookie is now set on a specific domain and not wildcard.