Please read the other comment threads that discuss this very thing

And with VPS you have to maintain the actual server. You can't just install it and be done. If you aren't already familiar with setting up servers, handling access, setting up software, and setting up DNS it will take you evening or two just to get going and after that it requires you continuous maintenance and how many of these custom forums actually have backups in case something goes wrong?

Then you have to pay for a domain name (which granted is cheap), setup something to handle your IP changes, install and maintain the pi itself and hope there aren't any vulnerabilities that can be exploited to gain a foothold in your home network, which means segragating it behind a VLAN which your ISP router probably doesn't support so you need to buy a router then of course you need to buy the pi it self and an SD card and powersuply since the normal micro-USB doesn't provice enough juice, but then again you didn't know that when you started. Then you probably want to buy a case for it so you don't just store a naked PCB on a shelve/floor. Then of course you need to setup the software and learn how it works and keep it up to day forever.

Or you can just spin another Discord "server" which you already know how to do and not have to worry about hosting anything.