feat(terraform): manage NEXT_PUBLIC_BACKEND via Terraform

Adds vercel_project_environment_variable.backend_url with value=""
to infra/terraform/vercel.tf. The frontend code uses
process.env.NEXT_PUBLIC_BACKEND as a prefix for fetch() calls;
an empty value forces relative URLs (e.g. /login), which Vercel
then rewrites to the backend via vercel.json.

Previously documented as a manual Vercel dashboard step; now
managed in version control alongside the rest of the env vars.

terraform validate: passes.

Author: Long104

infra/terraform/vercel.tf

@@ -24,10 +24,13 @@ resource "vercel_project_environment_variable" "frontend_url" {
   sensitive  = false
 }
 
-# NOTE: NEXT_PUBLIC_BACKEND is set to "" in the Vercel dashboard
-# (Settings → Environment Variables). It's not in this Terraform
-# because path-based routing means the frontend uses relative URLs.
-# Set it in the dashboard:
-#   Key:   NEXT_PUBLIC_BACKEND
-#   Value: (empty)
-#   Target: Production
+# Path-based routing: the frontend uses relative URLs (e.g. /login,
+# /google_login). Vercel rewrites them to the backend via vercel.json.
+# Setting this to "" forces the frontend to use relative paths.
+resource "vercel_project_environment_variable" "backend_url" {
+  project_id = vercel_project.senzen.id
+  key        = "NEXT_PUBLIC_BACKEND"
+  value      = ""
+  target     = ["production"]
+  sensitive  = false
+}