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>

.dockerignore

@@ -1,9 +1,9 @@
 # Root build context is used only by web/Dockerfile, which needs web/ and
-# docs/api/openapi.json. Allowlist those; keep everything else (target/, .git, crates)
+# api/openapi.json. Allowlist those; keep everything else (target/, .git, crates)
 # out of the context upload.
 *
 !web
-!docs/api/openapi.json
+!api/openapi.json
 web/node_modules
 web/.output
 web/dist