feat: Isolate dev build from prod (#83961)
### Why?
When running a dev server, it currently gets interrupted when running
`next build`.
This is very common when using AI for app development, where it runs
`next build` for whatever reason while the user is working on a dev
server.
### How?
This PR creates an isolated `dev/` directory inside the `distDir` to be
isolated from the build, and will not be cleared out during the `next
build` like the `cache/` directory. Since the cache between the dev and
prod isn't shared at the moment, it makes sense to let them have
separate `cache/` directories.
https://github.com/user-attachments/assets/2005ba70-861c-4763-b47f-cf17c62c0571
