observability: add structured diagnostics to scheduler loop and heartbeat-timeout detection

[prince8273]

Currently the scheduler loop and heartbeat-timeout detection emit minimal
context, making production diagnosis of stalls, slot contention, and worker
crashes difficult.

Changes

_do_scheduling()

• Captures dag_runs_examined after fetching active runs
• Emits scheduler.dag_runs.examined and scheduler.executor.open_slots gauges
• Adds a structured summary log line before return

_purge_task_instances_without_heartbeats()

• Emits scheduler.tasks.heartbeat_timeout gauge
• Enriches the existing error log with heartbeat_age_seconds, hostname,
  pid, and task_running_seconds

Notes

• Additive only — no behavior change, no state transitions affected
• Follows existing stats.gauge naming and import conventions

[boring-cyborg]

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[potiuk]

@prince8273 Converting to draft — this PR doesn't yet meet our Pull Request quality criteria.

• ❌ Other failing CI checks — Failing: Postgres tests: core / DB-core:Postgres:14:3.10:Core...Serialization, MySQL tests: core / DB-core:MySQL:8.0:3.10:Core...Serialization, Sqlite tests: core / DB-core:Sqlite:3.10:Core...Serialization, Low dep tests:core / All-core:LowestDeps:14:3.10:Core...Serialization, Integration and System Tests / Integration core otel. See docs.
• ❌ Pre-commit / static checks — Failing: CI image checks / Static checks. See docs.

See the linked criteria for how to fix each item, then mark the PR "Ready for review". This is not a rejection — just an invitation to bring the PR up to standard. No rush.

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Note: This comment was drafted by an AI-assisted triage tool and may contain mistakes. Once you have addressed the points above, an Apache Airflow maintainer — a real person — will take the next look at your PR. We use this two-stage triage process so that our maintainers' limited time is spent where it matters most: the conversation with you.

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Drafted-by: Claude Code (Opus 4.7); reviewed by @potiuk before posting