NYT is a pretty solidly right wing organization (eg [1] and [2]) like most for profit media outfits in the US. I suspect they’ll react like any other for profit business. Previous leaks have shown this to be the case [0][3]

0:https://www.theguardian.com/media/2022/feb/01/leaked-message...

1: https://citationsneeded.libsyn.com/news-brief-boudin-recall-...

2:https://citationsneeded.libsyn.com/news-brief-the-battle-ove...

3:https://actionnetwork.org/letters/new-york-times-stop-union-...