Formula executions can be queried only by the ObjectID from the trigger of the formula execution. You cannot query by ExecutionID. To query an ObjectID to return the expected formula execution, the ObjectID in the trigger event must have been recorded within at least the last three days and at most the last seven days, since this is the maximum amount of time those values are stored. Furthermore, the ObjectID in the trigger must have been generated by a polling or webhook event. If you manually triggered a formula, then this query by ObjectID cannot locate the event and no formula executions will be returned by the query.
Refer to this short recording as an example. In this scenario a poller is running and receives a new event that triggers a formula execution; the objectId from the poller event aligns with the formula execution trigger and a query retrieves the expected formula execution. Note that if you have a Notified event that contains multiple ObjectId’s in the events array then a query of Formula Executions for any one of those ObjectIds will result in all formula executions being returned that are associated with that entire Notified event. The formula execution query retrieves executions based on the event level.