HPV tests are of low value (as an adult, if ever sexually active, you likely have it but can do nothing about it); a new biomarker test that can detect the cancers is being developed [1]. Ongoing cancer surveillance is all you can do once exposed without having been vaccinated (and if cancer occurs, immunotherapy).

As pm90 wrote, I strongly recommend getting vaccinated [2] unless a doctor tells you otherwise, even if you already have HPV or have had previous potential exposure.

[1] Circulating tumor human papillomavirus DNA whole genome sequencing enables human papillomavirus-associated oropharynx cancer early detection - https://academic.oup.com/jnci/advance-article-abstract/doi/1... | https://doi.org/10.1093/jnci/djaf249

[2] https://en.wikipedia.org/wiki/HPV_vaccine

(had three doses in my 30s via Planned Parenthood)