[VS Code] Prompt cache clock doesn't reset after a /btw side question

Environment

• Claude Code for VS Code extension (Anthropic.claude-code) v2.1.301
• Subscription with 1h prompt cache TTL

What happens
In the VS Code extension, the Prompt cache clock next to the main input keeps counting down after I ask a /btw side question. It only resets after a normal main-conversation turn.

Why I think the clock is wrong
/btw reuses the main conversation's cached prefix. In the CLI, a /btw request shows a near-full cache hit plus a small 1h cache write, e.g.:

• input_cache_read: 453,691 (hit rate 99.76%)
• input_cache_write_1_h: 643

Since a cache read refreshes the entry's TTL, the main prefix is actually warm again, but the clock still shows it as about to expire.

Expected
The clock resets after a /btw (side panel) request that reads the main prefix, or the docs explain that side questions are not counted.

Why it matters
People who keep sessions warm on purpose (e.g. with auto/idle compaction turned off) rely on this clock to decide when to send something. Right now it shows the cache as colder than it really is.

Steps to reproduce

1. Start a long session in the VS Code extension and note the Prompt cache clock.
2. Wait some minutes, then ask a /btw question in the side panel.
3. The clock does not reset, while usage logs show a cache read on the /btw request.