[Fix] Custom automation search fails after timezone cadence update

[roomote-roomote]

​Opened on behalf of @daniel-lxs. Follow up by mentioning @roomote-roomote, in the web UI, or in Slack.

What changed

• Pass the deployment's effective scheduling timezone when custom automation cadence text is included in unified-list search terms.
• Cover searching a saved non-UTC cadence by its timezone label.

Why this change was made

PR #2444 changed the cadence formatter to require a timezone, while newer unified automation search code on develop still called it without that argument. The individually clean merges therefore produced a web typecheck failure after integration.

Impact

Custom automation search remains type-safe and can match the same timezone-aware cadence users see on saved automation cards. The focused component suite, web typecheck, formatting, lint, and repository pre-push gates pass.

Related PRs

• [Fix] Custom automation cards show cadence in the wrong timezone #2444: timezone-aware saved automation cadence
• [Fix] Custom automation results stay stale when user runs them now #2446: bounded refresh of persisted automation results

[roomote-community]

No code issues found. See task

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