I lived there in 2016, next to the Rite Aid outside (or maybe inside?) the CHAZ. The homeless situation was absolutely terrible for an American city. Sure it's not as bad as shanty towns I've seen in India or Malaysia, but it wasn't good. Housing was/is insane with shared rooms anywhere near the city being $700 and a 1 bedroom to yourself going for ~$2k. Not as bad as SF/The Bay, but still not good by any means.
Sure it's not "overrun," but there are a lot of them, and not enough jobs or affordable housing.
People complained about homeless people coming into the city for the benefits and I thought that was just a myth the Amazon employees would spew, but I talked to a social worker who told me that's true and that her office dealt with a lot of people who came to Seattle because of their programs and benefits.