Remove web-server from edge-ssr-app (#81389)
Continues https://github.com/vercel/next.js/pull/80915 removing the
final usage of `web-server` from `edge-ssr-app`.
Validated against our deploy E2E tests here
https://github.com/vercel/next.js/actions/runs/16428349930/job/46424359435
and
https://github.com/vercel/vercel/actions/runs/16428657423/job/46425277718?pr=13582
Closes PACK-1824
