Remove cloud provider text from project cards (#50754)

Project cards and the project table showed the raw cloud provider
(`AWS`, `AWS_K8S`) alongside the region, which is an internal
implementation detail. Both now show the region only — matching the
table's existing "Region" column header.

Fixes FE-4441

<!-- This is an auto-generated comment: release notes by coderabbit.ai
-->

## Summary by CodeRabbit

* **Updates**
  * Project cards now display the project’s region directly.
* Project tables show only the region in the region column, with “N/A”
when unavailable.

<!-- end of auto-generated comment: release notes by coderabbit.ai -->

apps/studio/components/interfaces/Home/ProjectList/ProjectCard.tsx

@@ -21,7 +21,6 @@ import { getManagedByFromOrganizationPartner } from '@/data/organizations/manage
 import { ProjectIndexPageLink } from '@/data/prefetchers/project.$ref'
 import { getComputeSize, OrgProject } from '@/data/projects/org-projects-infinite-query'
 import type { ResourceWarning } from '@/data/usage/resource-warnings-query'
-import { useCustomContent } from '@/hooks/custom-content/useCustomContent'
 import { useIsFeatureEnabled } from '@/hooks/misc/useIsFeatureEnabled'
 import { BASE_PATH } from '@/lib/constants'
 import type { Organization } from '@/types'
@@ -47,12 +46,6 @@ export const ProjectCard = ({
   const router = useRouter()
   const { name, ref: projectRef } = project
 
-  const { infraAwsNimbusLabel } = useCustomContent(['infra:aws_nimbus_label'])
-  const providerLabel =
-    project.cloud_provider === 'AWS_NIMBUS' ? infraAwsNimbusLabel : project.cloud_provider
-
-  const desc = `${providerLabel} | ${project.region}`
-
   const { projectHomepageShowInstanceSize } = useIsFeatureEnabled([
     'project_homepage:show_instance_size',
   ])
@@ -120,7 +113,7 @@ export const ProjectCard = ({
                     </DropdownMenu>
                   </div>
                 </div>
-                <p className="text-sm text-foreground-lighter">{desc}</p>
+                <p className="text-sm text-foreground-lighter">{project.region}</p>
               </div>
               <div className="flex items-center gap-x-1.5 relative overflow-hidden">
                 {project.status !== 'INACTIVE' && projectHomepageShowInstanceSize && (

apps/studio/components/interfaces/Home/ProjectList/ProjectTableRow.tsx

@@ -162,9 +162,7 @@ export const ProjectTableRow = ({
           </div>
         </TableCell>
         <TableCell>
-          <span className="lowercase text-sm text-foreground-light">
-            {project.cloud_provider} | {project.region || 'N/A'}
-          </span>
+          <span className="lowercase text-sm text-foreground-light">{project.region || 'N/A'}</span>
         </TableCell>
         <TableCell>
           {project.inserted_at ? (