🛠️ fix: harden GitHub transport diagnostics

[ShigureNyako]

Summary

• Treat noisy gh auth status failures as doctor warnings when REST and GraphQL probes both succeed.
• Broaden retryable GitHub transport error detection and increase read retry attempts from 4 to 6.
• Keep GraphQL mutations at 4 attempts and steer transport diagnostics toward direct API probes.

Validation

• uv run ruff check .
• uv run ty check --error-on-warning src/gh_llm tests
• uv run pytest -q
• prettier --check README.md
• gh-llm pr view 79119 --repo PaddlePaddle/Paddle --auto-collapse-author PaddlePaddle-bot --auto-collapse-author Paddle-CI-Bot

[Copilot]

Pull request overview

This PR hardens gh-llm’s GitHub transport diagnostics and retry behavior, aiming to reduce false negatives in doctor output and provide more actionable follow-up steps when GraphQL/transport errors occur.

Changes:

• Adjust doctor to downgrade noisy gh auth status failures to a warning when both REST and GraphQL probes succeed.
• Increase retry attempts for GitHub transport failures (notably GraphQL-backed reads) and broaden retryable error detection (e.g., stream/TLS/proxy/5xx indicators).
• Update layered diagnostics messaging and suggested follow-up commands to prefer direct API probes over gh auth status.

Reviewed changes

Copilot reviewed 5 out of 5 changed files in this pull request and generated 3 comments.

Show a summary per file

File	Description
tests/test_cli.py	Adds/updates tests covering doctor warning behavior, expanded retry cases (e.g., stream errors), and new retry counts/messages.
src/gh_llm/github_api.py	Increases retry/backoff limits, adds mutation-specific retry cap, and expands retryable error detection (including stdout+stderr inspection).
src/gh_llm/diagnostics.py	Updates GraphQL transport diagnosis text and shifts suggested next steps toward direct REST/GraphQL probes; broadens transport pattern detection.
src/gh_llm/commands/doctor.py	Refactors probe execution and reconciles auth-status failures into warnings when API probes succeed.
README.md	Documents the new doctor warning behavior and updated “Try next” probe guidance.

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