fix(weave): prevent Claude async turn misattribution

[rgao-coreweave]

Summary

• Prevent promptless turns when system/init precedes a delayed async prompt.
• Defer only bootstrap init messages, keeping late background-task output out of the next turn.
• Add regressions for delayed init, transport failure, and stale task output.

Follow-up to #7665 and its review thread.

Validation

• Claude Agent SDK shard: 44 passed
• Ruff check and format: passed

Scenario	master	This PR
Delayed prompt	Mispaired turns	Correctly paired turns
Late task output	Attributed to next turn	Excluded from next turn

Breaking changes

None.

[codecov]

Codecov Report

❌ Patch coverage is 85.71429% with 2 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
.../integrations/claude_agent_sdk/otel_integration.py	85.71%	1 Missing and 1 partial ⚠️

📢 Thoughts on this report? Let us know!

[ro31337]

Approving with a caveat to think about the corner case here, maybe improve here, or follow-up, or ignore if it's not relevant. Other changes look good

[w-b-hivemind]

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