Question I’m a little confused

I have a few questions about HPV screening. I know that once we turn 30, HPV testing is usually done along with a Pap smear, but I’m confused about the reasoning behind it. If my Pap smear is normal, why does it matter whether I’m HPV positive? I understand checking for HPV if the Pap is abnormal, but I’m trying to understand the benefit of testing when the Pap is normal.
I also have questions about what a positive HPV test actually means. Does a positive result only detect an active, ongoing infection, or can it detect HPV that I was exposed to years ago and already cleared? For example, if someone got HPV at age 20 and their immune system cleared it, would that still show up as positive years later, or would only a persistent infection be detected?
Lastly, does having completed all three doses of Gardasil before becoming sexually active significantly change my risk of developing high-risk HPV or cervical cancer?