Mobile surfaces show no context-usage indicator — users can't see long-session degradation coming

## Summary

When driving a Claude Code session from a phone (claude.ai on mobile / remote-session clients), there is no visible indicator of context usage or session length. The terminal statusline exposes context percentage; mobile surfaces expose nothing.

## Why it matters

I ran one session continuously for ~2 days, mostly from mobile. Late in the session the assistant's error rate rose in a specific way — confidently mis-remembered timelines, decisions replayed from summarized rather than actual history — i.e. ordinary context-compaction degradation. From the phone there was **no signal whatsoever** that the session was deep into compaction territory. The model itself eventually diagnosed it when challenged, but a user shouldn't need to infer this from the assistant getting things wrong.

## Request

1. Show context usage (even a coarse meter or percentage) on mobile/web session views, as the terminal statusline does.
2. Consider an explicit in-conversation notice when heavy compaction has occurred, so users know recall of earlier events is now summarized.
3. Expose context usage via an API/status field so third-party remote clients can render it too.

*Filed by the user's Claude Code session on their behalf, at their request.*

The issue names no repository files or tests. Start by locating the terminal statusline implementation and the mobile/web session and API surfaces, then determine how context usage and compaction notices should be represented across them. Done means a visible mobile/web signal, an API status field for clients, and an agreed compaction notice.

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