The live-token-usage refactor (d30edfda5) merged the SSE-updated `task`
prop on top of `fullDetail` to keep tokenUsage/status fresh. SSE strips
`log` to [] (stripTaskListHeavyFields) for list payloads, so the spread
clobbered fullDetail.log and the Activity timeline rendered empty.
Carve `log` out of the merge alongside `prompt`. Adds a regression test
that simulates the SSE-stripped task prop with a populated fullDetail.
Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>