Can custom skills sync automatically between ChatGPT web and local desktop Codex?

I use custom skills in ChatGPT Work on the web and local Codex conversations in the Windows desktop app. My web-created skills don’t appear in the local desktop skill catalog. I want to edit a skill from either environment and have the other pick up the change automatically, without repeatedly exporting, uploading, or copying files. I still need desktop conversations to work with local files. I tested a workaround: keep the instructions in a shared Google Doc and have a desktop skill read it on every invocation. Reading and updating the document from both environments worked, but invocation was slow. For the same dictionary prompt, my observed timings were: Web’s directly installed skill: about 7 seconds. Desktop skill fetching instructions from Google Docs: about 51 seconds. Desktop with the full original skill installed locally, with the Google Docs reader disabled: about 9 seconds. These are individual runs, not controlled benchmarks, but I’d prefer synchronization outside the response process. Has anyone got automatic two-way sync working between ChatGPT’s web-managed personal skills and local desktop skills ? Is there a supported account setting, plugin workflow, or working third-party solution? If you have, could you share the setup, required plan/app version, and whether changes actually propagate in both directions? Git syncing between two local folders would only solve part of the problem.