Delete NYT cookie, refresh page. In Chrome and Firefox this is available in just a few clicks by clicking the area immediately to the left of the URL.

Firefox's "Containers On The Go" addon lets you spin up disposable tab containers (see "Multi-Account Containers") with a single click. This works wonders for sites with limited free reads; it's increasingly the only way Medium is browsable for me.

I just get "You're in private mode" notification even without cookies. Firefox Focus only has a private mode, and tbh I wouldn't turn it off even if I could.

You get downvoted for mentioning that but I'm with you. I'm finding the NY Times impossible. As i live in Europe it's not of sufficient relevance to me to take out a sub but I'd like to see the stories linked to here.

Aka more garbage that can be skipped.