Another 1.6 million people filed for unemployment benefits last week (833k regular state claims, not seasonally adjusted, and 759k under the Pandemic Unemployment Assistance program).
https://www.nytimes.com/live/2020/09/03/business/stock-market-today-coronavirus/watch-for-a-lower-figure-on-unemployment-claims-and-an-asterisk

Regular state claims (unadjusted) were basically flat last week. They've basically stalled out since early August.

Sizable jump in claims under the Pandemic Unemployment Assistance program (covers freelancers, gig workers, etc). That's been edging up for several weeks now and is now at its highest level since July.

Continuing claims under regular state unemployment programs continue to trend down. But remember that can be because of people's benefits expiring, not just because they're getting jobs. Nearly 1.5m people are now on various extended benefits programs.

You'll see the 881k number for seasonally adjusted regular state claims in a lot of outlets this morning. There's nothing wrong with that number! But it *cannot* be compared to earlier seasonally adjusted numbers, as discussed at length here: https://twitter.com/bencasselman/status/1300845260629737483