I had wart on my heel once - kinda annoyingly stubborn which finally removed/subdued by laser removal (nitrogen therapy did jacks). That’s HPV, right? And guess once inside you, it stays inside you, right?
HPV is a family of viruses. There are dozens and the vaccine targets, I think, nine. So, that probably was HPV, but it probably was not one of the members of the family which the vaccine targets, the vaccine is focused on the sexually transmitted variants, since these are associated with Cervical cancer in particular, and several other nasty cancers, plus the genital warts.
There are over 100 hpv strlins. Warts are one yes, butnot the strain in question (though there are reports the vaccine helps for warts too I have not seen science verify that)