The Windows version has an autotype feature - not sure if that has made it to the ports though. It's also not as smooth a flow as Lastpass, since there is a con

The Windows version has an autotype feature - not sure if that has made it to the ports though. It's also not as smooth a flow as Lastpass, since there is a context switch between browser and password manager (although I seem to remember that there used to be an extension offering Lastpass style access to Keepass for Firefox, possibly called KeeFox, or FoxPass?). I don't think any distinct software could automatically log out of sites - it would presumably come down to deleting cookies on sleep (or relying on the sites to have sensible session expiry times) - so I'm not sure that the password manager is the right tool for that. A password manager would protect the passwords for your accounts, but that's not the same as sessions for your accounts.