They're looking at national politics, and on that score, yes, the ST is liberal. When it comes to local politics the Seattle Times is conservative. Your objection is a bit like people who object that the Democrats are conservatives, from a European perspective, except this is about the city itself. The current mayor is liberal, the previous mayor was conservative. They're both Democrats and would be defined as liberals by your factcheck, but that's a different rubric than the one we're talking about.
As a European, Democrats are absolutely not conservative from a European perspective. There are multiple dimensions but at least socially they push everything further to the left than in Europe. (Which is also in my opinion why they are losing elections)
Almost every social topic is pushed to the extreme left by the Democrats. Simply look at how many weeks abortion is allowed in blue state and compare with most European countries. Most European countries are way more conservative.
Economically yes, they are more conservative but even that is now changing as well (see: New York and AOC).
Using local labels to communicate to an (inter)national audience is a bit foolish, I think.
In SF, we have a wealthy clique who are locally labeled as “progressives” and who are also contradictorily against new housing. They even veto’d building a new apartment complex on a parking lot!
I’d personally call that clique “NIMBY” since their “progressive” label is essentially designed for propagating denialism among the credulous.