The Raspberry Pi 4B consumes between 2.8 to 4 KWh per month (very cheap) but it can be a little higher depending on the load and connected peripherals.
BTW, I forgot to mention one important difference with regards to self hosting. You have to make sure you have a public IP assigned to your home router and configure port forwarding on it to redirect incoming traffic towards your server, also if your ISP doesn't assign you a static public IP (which is often the case for home services) you have to update the IP your domain (web address) points to every time it changes by using a DDNS service like noip for example.
If you decide to go the Raspberry Pi way, let me know, I have some useful resources for that in my blog.