fix(agent): add session initialization timeout diagnostics

[tatoalo]

Problem

session initialization timeouts currently surface a generic error. This makes it difficult to tell whether SDK startup, model configuration, or gateway setup stalled.

Changes

• Add structured initialization phase, timing, model, timeout, and gateway-presence fields to failure logs
• Preserve query termination behavior and add regression coverage for timed-out initialization

[trunk-io]

😎 Merged successfully - details.

[github-actions]

React Doctor found no issues in the changed files. 🎉

_{Reviewed by React Doctor for commit 1f97624.}

[greptile-apps]

_{Reviews (1): Last reviewed commit: "fix(agent): add session initialization t..." | Re-trigger Greptile}

[github-actions]

Additive diagnostic logging and telemetry for session-initialization failures across three agent adapters, with matching regression tests (including an explicit test that secret error detail is never exported via telemetry); no auth, billing, crypto, dependency, CI, or API-contract changes, and diff matches the description.

• Author wrote 0% of the modified lines and has 105 merged PRs in these paths (familiarity MODERATE).
• 👍 on the PR from greptile-apps[bot].

Gate mechanics and policy version

Gate		Result
prerequisites	✓	all clear
deny-list	✓	no deny categories matched
size	✓	165L, 6F substantive, 399L/11F incl. docs/generated/snapshots — within ceiling
tier	✓	T1-agent / T1d-complex (399L, 11F, single-area, fix)
stamphog 2.0.0b3		.stamphog/policy.yml @ d4ace51 · reviewed head 1f97624