If the Otterbox case had a rubberized coating on it to try to improve grip, and with it being 6 years old, there’s a possibility it’s the culprit. You could try ditching the case for a little while, and/or getting a new case and swapping them out, clean the surfaces again and see if you feel the stickiness again after handling your phone and other stuff.

However, normally with those rubberized coatings, the degradation is more immediately apparent and you’d be more apt to avoid touching anything else afterward. Also in my experience I don’t recall it transferring to other surfaces much, but then again when I dealt with it I noticed ASAP and cleaned my hands right away.