With a VPS-self-hosted VPN all your connections to the outside originate from a static, unique, unshared IP, making it trivial to track and correlate your behavior across all protocols. Instead of containable identifiers like cookies, your IP has become a guaranteed unique identifier.

To leverage this, it's fairly easy to detect you're on a self-hosted VPN: your IP is in an IP range assigned to a hosting/colocation provider, is not a TOR proxy (there is a public list of those) and doesn't belong to any remotely popular VPN (easy to enumerate for a little money, lots of lists exist).

In exchange for that you have eliminated your ISP (or public wifi) as a threat but instead added the hosting provider to the list of threads. And for any adversary that stands above the law, the routing infrastructure of your hosting provider is already a valuable target.