fix: Fix stale context usage after compaction + usage calculation (#1548)

## Problem

1. Context usage calculation omitted output_tokens, under-reporting total token occupancy.
2. Context usage bar shows stale pre-compaction values until the next agent turn, making it look like context is still full after compaction.

## Changes

1. Include output_tokens in context usage calculation (they become input on the next turn)
2. Emit a usage_update with used:0 immediately on compact_boundary
3. Reset local usage counter on compaction so subsequent turns start fresh

## How did you test this?

Manually

Author: charlesvien

packages/agent/src/adapters/claude/claude-agent.ts

@@ -371,8 +371,18 @@ export class ClaudeAcpAgent extends BaseAcpAgent {
         switch (message.type) {
           case "system":
             if (message.subtype === "compact_boundary") {
+              // Send used:0 immediately so the client doesn't keep showing
+              // the stale pre-compaction context size until the next turn.
               lastAssistantTotalUsage = 0;
               promptReplayed = true;
+              await this.client.sessionUpdate({
+                sessionId: params.sessionId,
+                update: {
+                  sessionUpdate: "usage_update",
+                  used: 0,
+                  size: lastContextWindowSize,
+                },
+              });
             }
             if (message.subtype === "local_command_output") {
               promptReplayed = true;
@@ -530,6 +540,11 @@ export class ClaudeAcpAgent extends BaseAcpAgent {
             }
 
             // Store latest assistant usage (excluding subagents)
+            // Sum all token types as a proxy for post-turn context occupancy:
+            // current turn's output will become next turn's input.
+            // Note: per the Anthropic API, input_tokens excludes cache tokens —
+            // cache_read and cache_creation are reported separately, so summing
+            // all four fields is not double-counting.
             if (
               "usage" in message.message &&
               message.parent_tool_use_id === null
@@ -544,6 +559,7 @@ export class ClaudeAcpAgent extends BaseAcpAgent {
               };
               lastAssistantTotalUsage =
                 usage.input_tokens +
+                usage.output_tokens +
                 usage.cache_read_input_tokens +
                 usage.cache_creation_input_tokens;