Fix dead links and cleanup docs (#596)

* Add streaming response optimization spec for non-Next.js paths

* Address spec review: Content-Length, streaming gate, finalization order, rollback

* Address deep review: header timing, error phases, process_response_streaming refactor

* Address deep review: remove fastly::init, fix API assumptions, add missing paths

* Cleanup package files and update streaming response design spec

* Revert streaming response design spec formatting changes

* Fix dead links in spec docs after crate rename

Update stale crate paths (crates/common/ → crates/trusted-server-core/,
crates/fastly/ → crates/trusted-server-adapter-fastly/) and convert
source code file references from markdown links to backtick references
since vitepress cannot resolve paths outside the docs directory.

Author: aram356