At a few sites such as
I found the following definition of nevertheless:
Both "nevertheless" and "nonetheless" have the same basic concessive meaning as "however": They all introduce a sentence that gives information which is unexpected or surprising in light of information given in a previous sentence. Unlike "however", which is based on a positive-to-negative ordering of information,"nevertheless" and "nonetheless" require an opposite ordering of information, negative-to-positive.
But "nevertheless" is not defined in this way at dictionary sites, such as Oxford and Merriam-Webster, which just define its meaning as: "in spite of that: however".
I am not clear which definition is correct and complete.