HPV is considered an inevitability of sexual activity now, and you are smart to be asking about it.
Using a condom for anal sex can significantly reduce your risk of HPV, by at least 50%. That's not always realistic in a long-term relationship, though.
A lot of STDs aren't doing anal paps, though I agree that it's a valuable tool. Unless there is some reason that you don't want to disclose this to your PCP (like your sister's husband's cousin is the receptionist), then you should consider doing that. If it's impossible for you to do because of good reasons (that we don't need to know), then perhaps it's time to find another doctor. Find one who can address all your needs, and one you will be comfortable sharing all aspects of your health with.
I couldn't find much to support that numbers are increasing - and many times, increasing numbers of something only means that diagnostic tools are getting better, but in the US, only about 8,000 people are diagnosed with anal cancer each year. https://www.mdanderson.org/cancer-types/anal-cancer.html There are about 44,000 HPV-related cancers each year - https://www.cdc.gov/cancer/hpv/statistics/index.htm
I'm not an oncologist (or any doctor, for that matter), so I can't answer about progression of anal cancer. I can say it's rare, though, and something you probably don't need to overly worry about.