@nprofile1q... i mean, only sort of
I didn't read far enough to see if they analyzed what fraction of the resource consumption was due to sqlite, but whatever it was won't significantly increase if you split up logic and data so they run in separate processes. Given the performance work that goes into pg, there's a pretty good chance it actually goes down.
So there's nothing stopping you from running your app and pg on the same host. In which case, you're in basically the same compute condition as running sqlite inside your app. Except that now you have vastly more operational flexibility. You can have zero downtime backups. You can run two instances of your app, and so achieve zero downtime upgrades. You can scale that monolith to the limits of 2 machines, instead of 1. You can run 2 instances of the monolith for high availability. These things are impossible with one big sqlite file, and involve zero change to the app's architecture. And then if you do hit the limits of what you can achieve with one big db server, you have all the horizonal scaling options that pg gives you that still require little to no change to the application architecture. So you can do that in days, rather than months.