feat: Add online status display and context usage tracking to ChatInput

- Display connection status indicators (online, offline, thinking, permission required) in ChatInput with dynamic vibing messages
- Add context size percentage display showing remaining context availability
- Track latest usage data in reducer with inputTokens, outputTokens, cache metrics, and contextSize
- Calculate contextSize from message usage data and expose via latestUsage in reduceChatBlocks
- Pass thinking, agentState, and contextSize props to ChatInput component
- Remove redundant status indicators from SessionHeader (moved to ChatInput for unified display)

web/src/components/SessionChat.tsx

@@ -192,6 +192,9 @@ export function SessionChat(props: {
                 permissionMode={props.session.permissionMode}
                 modelMode={props.session.modelMode}
                 active={props.session.active}
+                thinking={props.session.thinking}
+                agentState={props.session.agentState}
+                contextSize={reduced.latestUsage?.contextSize}
                 onPermissionModeChange={handlePermissionModeChange}
                 onModelModeChange={handleModelModeChange}
                 onAbort={handleAbort}