Sidebar blanks Context, Limits and the footer for up to a second after /clear #243

What happens

After /clear, the Sidebar's Context and Limits bodies and the claude cli: … / ctui: … footer go blank for up to about a second, then come back together, Context at 0%. Live on 2.1.292 (tmux, sampling the pane every 50 ms from the /clear Enter): they vanish at about 115 ms and return at 171–1052 ms across 11 runs, with Limits cost auto and on, at release/0.5.0 and at v0.4.0. The "Run /clear" row of docs/testing/live-checks.md expects Context at 0% within a second and the footer to stay.

Why

/clear empties $.state with no session.start and no session.measure after it (a tagged probe in setUsage logged none). Only the 1 s $.clock.every tick refills usage and versions (refillUsage/refillVersions in ctui/hooks/register.tsx), so the gap is wherever the tick's phase falls. The engine does redraw the Sidebar as soon as $.state empties.

Ask

When the Sidebar's Pane render reads usage or versions as unset, schedule the matching refill from $.clock.after(0, …): render hooks never write $.state themselves. Keep the tick's refill. A probe of exactly this brought both back at 115–172 ms in 4 of 4 live runs. Update the existing test "after /clear empties $.state, the tick reloads the usage and the versions" (ctui/tests/usage.test.tsx) so the rows are back after a redraw and clock.settle(), with no clock.advance(1000). Ship it from bugfix/clear-refill, cut from release/0.5.0, with its pull request into release/0.5.0.