I was puzzled by this happening when I used Spotify on my PC, but not when I used it on any other device (phone, tablet, smart speaker). Today I went back into Spotify on my PC and noticed that I was already logged in (and no email arrived). So, I'm guessing that if I just turn off the app, which is what I would do on any other device, I stay logged in? The emails may well have been sent because I logged back in on my PC for the first time in a while? So, by taking the trouble to search for the menu, find 'log out' in the menu and then click it, I gave myself some extra trouble!