Support for Custom Client Identity on Schedule Trigger

Is your feature request related to a problem? Please describe.
We’re trying to differentiate between workflows triggered automatically by a schedule and those triggered manually—such as via the Temporal UI, API, or dashboard. While the TemporalScheduledStartTime search attribute helps in distinguishing scheduled runs in some scenarios, there’s currently no way to identify who or what initiated a manual trigger (e.g., via ScheduleHandle.trigger() or the UI). Additionally, interceptors like ScheduleClientCallsInterceptor.CreateScheduleInput don’t provide enough context to determine the trigger source.

Describe the solution you'd like
We’d like a metadata field—such as trigger_source or client_identity—to be added to the schedule trigger context. This would allow us to track whether a manual trigger came from the UI, a specific service, or another user.

Describe alternatives you've considered
As a workaround, we plan to compare nextActionTime with the actual workflow start time and then manually set a trigger_type search attribute within the workflow.

Additional context
Related Slack discussion: https://temporaltechnologies.slack.com/archives/C076CB0E075/p1747790772423569

Start by tracing the UI and API paths for manual schedule triggers, including ScheduleHandle.trigger() and ScheduleClientCallsInterceptor.CreateScheduleInput. Determine where trigger context is available and whether the UI can provide the requested identity; done means scheduled and manual triggers expose distinguishable source metadata for the stated callers.