wip: context-meter + model-label UI and provider/inference tweaks

Checkpoint of in-flight work so the orchestrator branch can rebase onto a
clean main: ContextBar → ContextMeter, model-label helper, model/agent picker
+ provider-snapshot/registry changes, inference payload + message-columns.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

apps/web/src/components/NewPaneMenu.tsx

@@ -21,7 +21,7 @@ export function NewPaneMenu({ onAddPane, disabled }: Props) {
         <button
           type="button"
           disabled={disabled}
-          className="inline-flex items-center justify-center min-h-[44px] min-w-[44px] rounded-full bg-muted/40 hover:bg-muted/70 text-foreground disabled:opacity-40 disabled:cursor-not-allowed shrink-0"
+          className="inline-flex items-center justify-center min-h-[36px] min-w-[44px] rounded-full bg-muted/40 hover:bg-muted/70 text-foreground disabled:opacity-40 disabled:cursor-not-allowed shrink-0"
           aria-label="New pane"
         >
           <Plus size={16} />