According to this university's website, there are four types of commas: listing, joining, gapping, and bracketing comma.
In the section dedicated to bracketing commas, there's this bit:
The problem is that the interruption in this sentence is only the sequence finding them; the word and is not part of the interruption, but an essential part of the sentence.
"... an essential part of the sentence" isn't a complete sentence (so it can't be a joining comma). Nor it's a weak interruption; if you leave the part after but, half of the meaning is gone (so it can't be a bracketing comma).
Therefore, I was expecting to see this:
... the word and is not part of the interruption but an essential part of the sentence.
What kind of comma is this? Maybe the author made a mistake based on his own comma rules?