fix(agent-server): handle follow-up turn failures and classify timeouts

[tatoalo]

Problem

When an agent turn crashed mid-prompt on a live follow-up message, the failure was effectively invisible:

• The follow-up user_message had no failure handling (unlike the initial/resume paths), so a thrown agent error just returned as an HTTP-200 JSON-RPC error
• The Claude SDK also surfaces the error string as an ordinary assistant message, so the crash rendered in the transcript as a normal reply so it looked like a healthy turn
• "API Error: ... timed out" was classified as a permanent agent_error rather than a transient upstream stall, so even retryable timeouts were treated as hard failures

Changes

• added an upstream_timeout classification
• introduce a single handleTurnFailure(payload, phase, error) used by the initial, resume, and (newly wired) follow-up paths
• the failure is always surfaced as a tagged error session update instead of riding the normal assistant-message path.

before:

after:

[github-actions]

React Doctor found no issues in the changed files. 🎉

_{Reviewed by React Doctor for commit d8639b4.}

[greptile-apps]

_{Reviews (1): Last reviewed commit: "fix(agent-server): handle follow-up turn..." | Re-trigger Greptile}

[greptile-apps]

_{Reviews (2): Last reviewed commit: "fix(agent-server): scope recoverable to ..." | Re-trigger Greptile}

[github-actions]

Focused, well-tested fix: adds timeout error classification, refactors failure handling to distinguish recoverable upstream errors in follow-up turns, and properly scopes recoverability to interactive mode only. No showstoppers; the one bot review comment was addressed and resolved.