So I don't use overseerr but I do use jellyseerr with my emby setup. Both are just webservers that use a webpage/site that you can login to and add/search for content that will then be sent to your -arr stack and finally indexed into Plex/Emby. You can install overseerr on whatever machine you like, but to access it your other devices need to know where to find it (ie IP:port of hosting machine). You should really set up overseerr on a machine that runs continuously, so like others have said, likely the machine you run Plex on.
I personally take this a step further and use an internal custom domain name (ie. jellyseerr.mymedia.com) that can be accessed from any device on my internal network. I set my router to capture all domain requests for "mymedia.com" and redirect them to a reverse proxy (swag in my case) that will then forward the requests to different IP:port combinations based on subdomain. For example: emby.mymedia.com, jellyseerr.mymedia.com, radarr.mymedia.com, etc. This allows you to access all your services using easy to remember domain names instead of IP addresses.
Awesome, but what's up with the chonk leg?