Nsec.app doesn't use nsecbunker (server-side nip46 server). It stores your keys in browser and runs nip46 server in a service worker, it's server only wakes the worker up when needed.

You could host your own version of nsec.app. But doing that just to sync your keys through your own server isn't worth it - sync is e2e encrypted with your password, you don't gain much from self hosting.