Migrate usage of web-server in edge-ssr (#80915)
This continues the work for the `handlers` interface for the edge
runtime and re-uses the existing `route-module` interface we have
instead of initializing and using `web-server`/`base-server`.
Validated against our deploy tests
https://github.com/vercel/vercel/actions/runs/15987684940/job/45095833866?pr=13505
https://github.com/vercel/next.js/actions/runs/15987664161/job/45095390463
