How do I automatically populate a field value based on another field value without using a picker in Oracle Sales in the Redwood User Experience?

You can add an on-picker-value-changed="" and set up a listener as the value. Pass in the raw event. The payload in your action chain of event.detail.event.detail.value (or .previousValue) will give you the key of the cx-picker DCL. Note the double event.detail is required because this event wraps an oj-select-single event.