As the article notes, writers for her show are governed under a separate contract which was not being struck.

No, you're misunderstanding that portion of the article.

The Actors agreement allows talk shows to continue with SAG/AFTRA members, but the writers strike covered the writers on the show. They tried to restart production without writers (which is possible, Late Night did it in the last writers strike).

So even though the Actors strike is still happening, shows like this can use union actors (like Drew Barrymore) now. And they can use union writers now, too, because the writers strike is over.