Replace f-string log calls to structured kwargs logs

[Dhanus3133]

Why

LOGGER calls across the backend used stdlib logging with f-string messages, so fields weren't queryable in JSON logs.

Closes #1131

What changed

• Replaced stdlib logging.getLogger() with structlog get_logger(); converted f-string log calls to structured kwargs on safe (non-Prefect) loggers, and added exc_info to exception logs.

Checklist

• Tests added/updated
• Changelog entry added (uv run towncrier create ...)
• External docs updated (if user-facing or ops-facing change)
• Internal .md docs updated (internal knowledge and AI code tools knowledge)
• I have reviewed AI generated content

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Summary by cubic

Replaced f-string logs with structured structlog kwargs and added exc_info to preserve tracebacks, making JSON logs easier to query. Addresses Linear 1131.

• Refactors
  • Switched stdlib logging.getLogger() to structlog.get_logger() where safe; flows use Prefect get_run_logger.
  • Converted logs to keyword fields across auth, diff/merge, git, GraphQL, migrations, tasks, webhooks, database, and HTTP client.
  • Standardized batch/query messages with clear fields (e.g., limit, offset, batch, num_nodes, refs) and added exc_info to errors/warnings.
  • Removed unused loggers in event and approval modules; updated webhook test to assert the structured duplicate-header warning.

^{Written for commit 4f5093a. Summary will update on new commits.}