There is many different strains of HPV, the likelihood of already have contracted them all is small. It will still protect you against strains you don't have. It also protects against genital warts. The vaccionation program targets young girls because thats the most efficient time to take it and has highest benefit/cost. You will still reap benefits of taking it later.

I dont see any reason not to take if you get it for free and you are planning to be sexually active with multiple different partners.

This. Protects against strains you don't have, reduces the spreading. We (male that have sex with females, and haven't been vaccinated) are a huge infection vector.

My doctors have generally refused vaccinating me for years (Male/43yo), but finally a new (female) doctor told me it's a good idea. I'm not in a risk group, so I have to pay for the vaccine: Gardasil 9, 3 doses, 3 months away of each other, ~€200 each, although studies say that 2 doses might be enough.

In reality, you can pay to a private doctor so they write you a prescription, but I feel more validated if my doctor says it's OK :)

just keep in mind that not all kinds of HPV vaccines protect against all the strains causing warts! Some do, but not all, check the specific brand you're getting! Obviously cancer is worse, but the extra protection is nice to have.