Is Strange New Worlds in a different universe than Star Trek

My impression is that Star Trek Strange New Worlds is for the most part trying to be consistent with the main events of the Star Trek original series, particularly the events outlined in the original pilot and what became the episodes known as The Menagerie.  The episodes in the new series do take place prior to the original series, so they have been adding characters and plot lines as they go.  I agree that they have embellished the relationship between Nurse Chapel and Spock.

Wikipedia has an article on Nurse Chapel, and they describe how the original series was not always consistent in how they portrayed the character, and the character evolved over time:

I believe you are referring to the events of the episode What Are Little Girls Made Of?, which is mentioned in the Appearances section.

There are other events in Strange New Worlds that lead to questions as to how they will eventually align with the beginning of the original series.  Recently they have had more episodes with a love interest for Captain Pike, for example, and this character does not appear in The Menagerie.

The creators of the new series have admitted that they have had to change some of the time line.  Back in the 60's the original series referred to some dramatic events happening in the near future that for us now don't make sense, so they are taking dramatic license to modify it a bit.  But to my knowledge they are not using the excuse that the series is a completely different timeline.