Can I just serve a Notice to Terminate Tenancy a/k/a “20-day” notice, and then call the sheriff/change locks?

No.

With the notice to terminate tenancy a/k/a “20-day” notice the landlord must go through the exact same court eviction process as with a 3-day notice to pay rent or vacate and/or 10-day notice to comply or vacate.

If the tenant does not comply with the notice, the notice to terminate tenancy is not a faster eviction process. It is slower.

A notice to terminate tenancy is only applicable if the tenancy is month-to-month. In Seattle, the landlord must also have just cause.