you’re right. Technically they aren’t a “Jewish” i.e. Judean sect, but rather they are a sect of Israelites - a sister religion to 2nd temple Judaism
and an “aunt religion” to both Christianity and modern day Judaism.
For me the revelation that modern day Judaism (modern-day meaning after 70 AD!!) is a sister religion to Christianity, and derived from Phariseeism explains a lot:
- like why there is more mention of Pharisees rather than Sadducees or Essenes in the Gospels - essentially the Pharisees (modern Judaism) were the other competitor sect
- like why “modern Jews” didn’t hold to the Messiah and at the same time didn’t have temple sacrifices