You can setup HTTP reverse proxy on your VPS. You’ll need to point the domain to your VPS for that to work.

What I really want is to be able to host multiple websites with my single home IP without those websites being obviously connected

That’s easy. You have two ways:

• Host the websites under different paths in the same domain. If your websites are static this is fine, but if they are “services” this may not be feasible (and could be very complicated if it is feasible).
• Host them under different sub-domains. The way it works is you create a bunch of NS records in your DNS, pointing the subdomains to your root domain, and setup one “virtual host” for each of them in your HTTP server. Both Apache and Nginx have the ability to match virtual host by domain name.

to avoid automatic bots constantly looking for vulnerabilities in my home network.

I’m not sure how you would eliminate bots by separating the websites though.