@Amir Zi I did some digging in guidelines and talked with our national underwriting team to get some specifics on FHA loans for your situation.
FHA does not allow the use of Rental Income from an ADU, short or long term even when reported on schedule E(tax returns). Rental income is allowed for Primary if 2-4 units or 1 unit investment.
To utilize rental income from your departing residence it would require an appraisal to show 25%+ in equity, 1007 Comparable Rent Schedule, & executed lease of at least 1 year.
The new primary multi-unit could use the same 1007 values for rent to help qualifying income, however a 1 yr lease is required.
Side note, depreciation shown on Schedule E can be added back for qualifying income for rental properties.
If you want to qualify any rental income from the departing residence FHA requires you be moving 100 miles away from the current/departing residence. You mentioned North Seatttle, so that would be moving to as South as Castle Rock/Longview(straight line) or as South as Napavine in 100 road miles.
I know that is a mixed bag of info, if you want to go deeper be happy to chat. :)