The split view (2+ sessions side by side) was lost on every refresh: its
pane set lived only in React state, and the one-shot ?split= deep link is
consumed on load. Persist the live session set to sessionStorage while the
split is the active view, and restore it on load when no ?split= deep link
is present, so a refresh brings the split back.
sessionStorage (not localStorage) is deliberate: it is scoped per browser
tab, so a split opened in its own tab and the in-window split never clobber
each other, and a fresh unrelated tab restores nothing — while still
surviving a refresh of the same tab. The ?split= URL stays the shareable,
cross-tab channel.
Only an explicit close (the split's back button) clears the persisted set;
detours to a single session keep it, so the split is treated as the user's
lasting context until they close it. Controlled hosts (which own their split
lifecycle) never auto-persist or auto-restore.
Co-authored-by: wenshao <wenshao@example.com>
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