Logseq DB is in the very early stages of alpha testing. We only test the browser version with our alpha testers at the moment; there are no local apps yet.
Regardless, none of your notes is sent to us when using that alpha version of Logseq DB. Everything runs local in your browser cache at the moment, so if you decide to use it make sure you backup often as data loss is still possible (for example when you empty your browser cache).