Fix task duration increasing forever after Dag run timeout skips it

[yuseok89]

closes: #58536

When a Dag run times out, unfinished tasks are marked SKIPPED but left with no end_date, causing the UI to show their duration growing indefinitely. Fixed by routing through set_state() which properly sets both end_date and duration.

Screenshots

Triggered a Dag with dagrun_timeout=60s and a long-running task, so the run times out while the task is unfinished and gets skipped.

• Before: the skipped task's duration keeps growing on refresh (no end_date).
• After: duration is fixed (~1m) with end_date set.

Before

After

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Was generative AI tooling used to co-author this PR?

• Yes (please specify the tool below)
  • Opus 5

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[steveahnahn]

LGTM. Fixes the growing-duration bug, and good test coverage, just one nit

[potiuk]

Hello @yuseok89 - thank you for your contributions to Apache Airflow!

The Airflow community has introduced a limit of 5 open pull requests at a time for contributors without write access to the repository. You currently have 11 open pull requests, so - as a one-time step of introducing the limit - we closed the ones where maintainers have not engaged yet:

• Add deferred task resume flow to task lifecycle diagram #65323 - Add deferred task resume flow to task lifecycle diagram
• Add TaskGroup-level retries to retry a whole group as a unit #68139 - Add TaskGroup-level retries to retry a whole group as a unit
• Dedent task docstrings used as doc_md #71108 - Dedent task docstrings used as doc_md
• Fix task duration increasing forever after Dag run timeout skips it #71549 - Fix task duration increasing forever after Dag run timeout skips it
• Ignore task start_date and end_date on manual runs #71758 - Ignore task start_date and end_date on manual runs
• Make HttpSensor defer when response_check is provided #71922 - Make HttpSensor defer when response_check is provided
• Flag ui-field-behaviour drift between hooks and provider.yaml in static checks #72089 - Flag ui-field-behaviour drift between hooks and provider.yaml in static checks
• Skip GCS folder-marker keys in GCSToSFTPOperator #72638 - Skip GCS folder-marker keys in GCSToSFTPOperator
• i18n(ko): Add missing translations (Sep25) #73677 - i18n(ko): Add missing translations (Sep25)

These pull requests stay open because maintainers are already engaged in them - they count towards your limit:

• Show recent task states on the Dags list page #69619 - Show task state counts for the latest Dag run on the Dags list page
• UI: Add a time-window scope to the Dags list run state filter #70470 - UI: Add a time-window scope to the Dags list run state filter

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Drafted-by: Claude Code (Opus 5); reviewed by @potiuk before posting