[kaluli123123]

Summary

• Persist activity on UserInput before its echo, and notify session metadata subscribers after timestamp changes.

Closes #57.

Root cause

Activity timestamps were updated only when a completion finished; set_last_updated also omitted the session-change notification.

Test plan and evidence

• RED before repair: Timestamp stayed at 2000 before the input fix; SessionsUpdated timed out before adding the store notification.
• Focused: 2 new user_input regressions passed, covering persistence before completion and SessionsUpdated without completion.
• Runtime: Actual client-channel cargo-run smoke emitted SessionsUpdated before model completion: last_updated=2026-11-03T09:41:34.685148+00:00, followed by ResponseDone.
• Rust formatting, workspace Clippy with warnings denied, and all-target compilation passed through ./check.bash.
• cargo test --locked --all-targets --no-fail-fast: 357 passed, 7 failed, 0 ignored. The exact same seven snapshot failures independently reproduced on clean base 1abc6fcff1f186124f924b56aa92c3a3684c90c5 (355 passed, 7 failed, 0 ignored), across tui_reflow_snapshots (6) and tui_submit_wrap_snapshots (1). No snapshots or thresholds were changed.
• cargo test --locked --doc: 45 passed, 1 ignored.
• Independent read-only review: no blocking findings.

Changed files

• crates/infinity-daemon/src/session/observer.rs
• crates/infinity-daemon/src/session/tests.rs
• crates/infinity-daemon/src/memory_store.rs
• docs/docs/infinity-code/background-agents.md

Remaining gates

Draft: required full checks are not green. Remote CI and maintainer review remain outstanding. Docs/UI Prettier were skipped by the repository script because node_modules are absent; optional browser e2e and THIRD-PARTY verification were not reached after the test gate failed. No live model account was used.

One independent commit from base 1abc6fcff1f186124f924b56aa92c3a3684c90c5. No dependency or wire-protocol changes. No merge, deployment, or Issue closure performed.