fix(agent-sidebar): restore width+open on reload, add deleteConversation

[I-am-nothing]

What

Fixes three independent cross-host agent-sidebar defects (all against v0.5.6), plus the review follow-ups.

Defect 1 — width not restored on reload

SidebarProvider's mount fetch only set lastOpenWidth, never the rendered sidebarWidth, so a persisted width was stranded until the next open gesture (close-then-reopen restored it; a reload did not). Now the fetched width is reconciled into rendered state via a guarded functional updater (setSidebarWidth((cur) => (cur <= 0 ? stored : cur))) so a user gesture that lands before the async fetch is never clobbered — first writer of a real width wins.

Defect 2 — open flag dropped on reload

AppShell derived visibility purely from width, with no controlled-open prop, so the shell always painted closed regardless of the persisted open flag both host session hooks already expose. Added open? / onOpenChange? to AppShellProps, derive isOpen = open ?? (sidebarWidth > 0), seed/collapse width via an effect when controlled open flips, and fire onOpenChange from the FAB (open) and close handlers. Uncontrolled (open === undefined) behavior is unchanged.

Defect 3 — remove conversation had no transport

The trash-icon delete button already shipped but nothing backed it. Added deleteConversation to the AgentChatClient contract and useAgentChat (optimistic history removal + open-thread clear, rollback on failure), re-exported through useAgentSession.

Root cause

Width and open were two separate pieces of state, but only width was being rehydrated and only width drove rendering. The persisted open flag had no path into the rendered shell, and the persisted width landed in reopen-memory (lastOpenWidth) rather than the rendered sidebarWidth. Reload reads both from the server but the shell discarded both signals. The fix routes the persisted width into rendered state and adds a controlled-open contract so the host's persisted open flag actually paints.

Review follow-ups (second commit)

• BLOCKING fix: the legacy persistKey localStorage unit test (SidebarProvider.test.tsx > "does not read localStorage at module load") still asserted width === 0 after mount — the pre-fix behavior. Defect 1's reconcile now restores the persisted 500 into the rendered width over a defaultWidth of 0, so the assertion + comment were updated to expect 500. The equivalent server-persistence test was already updated; this legacy path was missed and was landing main red (1/768 failing). Suite is now green (768/768).
• Consistency: deleteConversation rollback switched from a full-list overwrite to a MERGE updater (mirrors renameConversation), re-inserting the removed row at its original index — preserves any conversation created between the optimistic drop and a failed network call. Behavior-identical in the common case.
• Clarity: two AppShell.tsx comments tightened (controlled-open effect dep rationale; the load-bearing sidebarWidth > 0 panel guard). No behavior change.

Verification

• pnpm test — 768/768 passing (was 767/768 with 1 red)
• pnpm typecheck — clean
• pnpm build — clean

Versioning

No package.json version bump and no CHANGELOG touch. These kit changes ride a later 0.5.7 rollup release, not this PR.

DRAFT — cross-repo merge order

This sidebar fix is part of a coordinated cross-repo change. Land in this order:

1. api-platform
2. api-client-shared
3. web-ui-kit ← this PR
4. web-applications
5. web-account

Why draft: web-ui-kit depends on the upstream repos' unpublished releases landing first (api-platform, then api-client-shared). Keep this as a draft until those two are merged and the dependent release/contract is available. Un-draft once api-platform and api-client-shared have landed and this can ride the 0.5.7 rollup release into web-applications / web-account.

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Storybook Preview: https://mirrorstack-ai.github.io/web-ui-kit/pr/305/