Currently, all other smart values listed under the sprint section of the following link:

https://support.atlassian.com/cloud-automation/docs/jira-smart-values-development/#--sprint--

Appear to work and return correct values regardless of the trigger used. However, sprint.originBoardId only works if a sprint based trigger is used. This smart value should be able to be accessed the same as the rest of the smart values regardless of what the trigger is since the data being accessed for that shouldn't have any issues being used if the trigger is "field changed" or something else.