Any documents, including powers of attorney, can be recorded with the recording office if the documents meet the formatting requirements and fees are paid. In general, powers of attorney are not recorded.
Many counties in WA have their recorded documents available for viewing online. If not available online, the documents are available at the recorder's office.
The recorded documents would be indexed under the names of the principal (the person giving the power) and the agent (person given the power).
If the agent is working with you on behalf of the principal, you can ask for a copy of the document.