fix(sidebar): read betterSidebar via ctx.get() in all internal consumers

Under the DSH 0.1.1-rc.x web shell, the Cordis plugin loader registers
the provided betterSidebar impl on a neighboring fiber that is not on
the rendering fiber parent chain, so every direct ctx.betterSidebar
read inside the plugin own tree throws

  cannot get property "betterSidebar" without inject

and the panel dies inside RenderBoundary on page load (observed with
0.14.0 and 0.15.2 on npm-installed dsh 0.1.1-rc.2). This is the same
failure class #135 fixed for the dsh-web-mobile path; declaring
betterSidebar in the plugin own inject would deadlock the fiber (it
waits for the service before running apply, but the service is only
provided inside apply).

ctx.get() resolves through the root reflect store and is unaffected by
the fiber chain, so all 26 internal reads switch to it. External
consumers keep using ctx.betterSidebar after injecting it, unchanged.
Test mocks gain a matching get() shim.

src/client/SideChatView.tsx

@@ -295,7 +295,7 @@ export function SideChatView(props: {
     setError(null)
     try {
       const { childId } = await api.sidechatStart(scope.sessionId)
-      ctx.betterSidebar?.updateTab(tab.id, { meta: { threadId: childId } })
+      ctx.get('betterSidebar')?.updateTab(tab.id, { meta: { threadId: childId } })
     } catch (cause) {
       setError(cause instanceof Error ? cause.message : String(cause))
     } finally {
@@ -319,7 +319,7 @@ export function SideChatView(props: {
     const title = threadDisplayTitle(display)
     if (title !== '' && title !== tab.title) {
       try {
-        ctx.betterSidebar?.updateTab(tab.id, { title })
+        ctx.get('betterSidebar')?.updateTab(tab.id, { title })
       } catch {
         // A stale title is cosmetic; the thread keeps working.
       }
@@ -422,7 +422,7 @@ export function SideChatView(props: {
    *  creates the thread on mount). */
   const openNewThread = (): void => {
     setMenuOpen(false)
-    ctx.betterSidebar?.openTab({ type: 'sidechat' }, scope)
+    ctx.get('betterSidebar')?.openTab({ type: 'sidechat' }, scope)
   }
 
   /** Switch to an existing thread: parked for createTab, deduped to the
@@ -431,7 +431,7 @@ export function SideChatView(props: {
     setMenuOpen(false)
     if (id === threadId) return
     parkSidechatReopen(id)
-    ctx.betterSidebar?.openTab({ type: 'sidechat' }, scope)
+    ctx.get('betterSidebar')?.openTab({ type: 'sidechat' }, scope)
   }
 
   const menuItems = useMemo<MenuEntry[]>(() => {