Validate iOS Safari SPA-nav logo fix on docs site

[tony]

Summary

• Pin gp-sphinx and sphinx-gp-theme (and transitive workspace siblings) at unreleased gp-sphinx ref 652ce020 on branch fix/spa-nav-ios-relative-urls. The fix reorders pushState above swap(doc) in spa-nav.js so relative href/src in the swapped DOM resolve against the new baseURI.
• Temporarily add this branch to the docs workflow trigger so the rebuilt site at https://libtmux-mcp.git-pull.com serves the patched theme.

Background

On iPad Safari (landscape, or "Request Desktop Site" — viewport ≥ 63em where Furo's sidebar drawer is on-screen), the sidebar logo blanks after every cross-depth SPA navigation. Sphinx emits page-relative logo paths (e.g. _static/img/libtmux.svg on root, ../_static/img/libtmux.svg on /api/), and the previous order ran swap(doc) before history.pushState, so setAttribute("src", …) resolved the new path against the old document.baseURI and produced a 404 on the wrong directory.

Chromium and Gecko queue <img src> resolution as an element task and read baseURI after pushState runs on the same call stack, so they tolerate the bug. WebKit on iOS resolves eagerly at setAttribute time, and inside document.startViewTransition the failed-load state is then committed into the new snapshot during the 150ms cross-fade.

Test plan

• Wait for the docs workflow to deploy this branch.
• On an iPad Safari (landscape, viewport ≥ 1008px so the sidebar drawer is on-screen), open https://libtmux-mcp.git-pull.com/ and click an internal link that crosses directory depth (e.g. root → /api/, /installation/ → /).
• Confirm the sidebar logo persists across the cross-fade transition (before this fix, it blanks).
• Repro on Chromium DevTools at 1024×768 with Network filter on _static/img/libtmux.svg — no 404 entries during cross-depth nav.

Follow-ups (not in this PR)

• Drop the ci(docs[temp]) commit (and the try/spa-nav-ios-fix branch entry in docs.yml) before merge.
• Replace the [tool.uv.sources] git pin with the released gp-sphinx==0.0.1a12 pin once it ships.
• Land https://github.com/git-pull/gp-sphinx/tree/fix/spa-nav-ios-relative-urls into gp-sphinx and cut the release.

[codecov-commenter]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 83.77%. Comparing base (669fbc2) to head (ba1e5a9).

Additional details and impacted files

@@           Coverage Diff           @@
##             main      #30   +/-   ##
=======================================
  Coverage   83.77%   83.77%           
=======================================
  Files          40       40           
  Lines        2132     2132           
  Branches      270      270           
=======================================
  Hits         1786     1786           
  Misses        266      266           
  Partials       80       80           

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