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>

design/windows-host-rewrite.md

@@ -428,5 +428,5 @@ This file replaces five docs (recoverable from git history):
 - `windows-host-rewrite-game-capture-bug.md` (the GB1 investigation + fix) — **fixed**; the resolution is
   §2.5 (capture). The full investigation narrative is in git history.
 
-(The older `docs/windows-host.md`, a pre-rewrite implementation plan from 2026-06-22, is a separate
+(The older `design/windows-host.md`, a pre-rewrite implementation plan from 2026-06-22, is a separate
 lineage and is left as-is.)