Add used/full context meter to chat screen (#717)

* Adopt /api/health REST route (issue #713)

Cheap liveness probe on the connection screen: GET /api/health surfaces
backend version + auth mode (Token vs Gated/OAuth) without the heavier
/api/status payload. Added HermesApiService.getHealth + HealthStatus model;
ConnectViewModel.loadHealth probes on open (best-effort, silent on failure);
ConnectScreen shows a read-only health card when reachable.

Verified: ktlint clean, assembleDebug BUILD SUCCESSFUL locally.

* Add used/full context meter to chat screen

Shows session prompt tokens vs model context window above the composer,
polled every 5s. Color-coded bar warns at 70%/90%.

* fix(chat): fix unit tests for context usage meter

Format >=100k tokens cleanly in ContextUsageChip and stub AuthManager profile ID in ChatViewModelTest.

* Fix context meter: source used tokens from input_tokens

Gateway /api/sessions/{id} has no last_prompt_tokens column; use
input_tokens instead. Show meter as soon as full context is known.

* Add tappable context breakdown sheet

Chip opens a bottom sheet with input/output/cache/read/write/reasoning
token rows + message count. Source breakdown from /api/sessions/{id}.

* Refresh context meter on streaming complete

Trigger fetchContextUsage immediately when a message finishes streaming
instead of waiting for the 5s session-sync poll.

* Fix context meter: source used tokens from live WS session.info

The REST /api/sessions/{id} endpoint reads the DB input_tokens column,
which is stale/0 for active sessions — that's why the meter was stuck at 0.

Switch the meter to the live values the gateway pushes over the WS
session.info payload after each turn:
- used = last_prompt_tokens (real used context for the turn)
- full = context_length (model-accurate window; keep /api/model/info as a
  fallback before the first turn completes)

fetchContextUsage now only tops up the denominator from /api/model/info and
no longer overwrites the live WS value with the stale REST input_tokens.
The 5s poll remains as a fallback.

* Revert "Fix context meter: source used tokens from live WS session.info"

This reverts commit 932393fd80993d57e66fe93552a949460d646674.

---------

Co-authored-by: M57 <hy4ri@users.noreply.github.com>

app/src/main/res/values-ko/strings.xml

@@ -179,6 +179,10 @@
     <!-- Connect Screen -->
     <string name="connect_selected_profile">프로필: %1$s</string>
     <string name="connect_action_select_profile">저장된 프로필 선택</string>
+    <string name="connect_health_title">백엔드 상태</string>
+    <string name="connect_health_body">Hermes %1$s · %2$s</string>
+    <string name="connect_health_auth_gated">게이트(OAuth)</string>
+    <string name="connect_health_auth_token">토큰</string>
 
     <!-- Connect Error Messages -->
     <string name="connect_error_token_required">토큰이 필요합니다</string>