Note that is $158/year, or $13/month.

Depending on how good you are with server admin-ish stuff, you might want to get a digital ocean VM instead, and set up a wireguard server there. As a bonus, you'd be able to put some simple logic (for example, if you are serving website from home computer, you could generate an error page if your home internet is not working)

That is correct, CHF prices are more or less the same as USD nowadays.

In case it matters for you: Compared to DO this service is running on a zero carbon infrastructure and your IP address is located in Switzerland.