fix: complete the docs/→design/ and openapi→api/ rename references

The file moves (docs/ → design/, docs/api/openapi.json → api/openapi.json) landed
in d01a8fd, but the matching reference updates did not — so mgmt.rs's drift-test
`include_str!("../../../docs/api/openapi.json")` pointed at a path that no longer
exists and the host failed to build. This restores it and updates every reference:

  - mgmt.rs include_str! → ../../../api/openapi.json (fixes the build)
  - web/orval.config.ts codegen target, web/Dockerfile, .dockerignore
  - deb/rpm/Arch packaging install paths
  - CLAUDE.md, the .gitea CI workflows, code doc-comments, design-doc cross-links

docs-site route URLs (/docs/...) untouched.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

packaging/bazzite/README.md

@@ -257,7 +257,7 @@ journalctl --user -u punktfunk-host -f
 
 > ⚠️ **There is no firewall script or firewall doc in the repo.** The ports below are derived
 > directly from the code constants (`crates/punktfunk-host/src/gamestream/mod.rs`, `mgmt.rs`) and
-> the GameStream-host port-map (`docs/gamestream-host-plan.md`). Treat the `firewall-cmd` lines as recommended-but-verified,
+> the GameStream-host port-map (`design/gamestream-host-plan.md`). Treat the `firewall-cmd` lines as recommended-but-verified,
 > not a checked-in script.
 
 **GameStream / Moonlight ports** (fixed; Moonlight derives them from the HTTP base). These only apply