sorry balloni, but I cannot help here. Point of used system called "o-auth" is, that Locus has absolutely no idea what is your username or password. Only what Locus knows is some generated nonsense key called "token", that is used for communications with groundspeak server.
Fact that you do not see any request on name or password on third screenshot, is probably because you checked "keep logged" during previous login, so it is not needed anymore. Try to tap on top button "refresh" (arrows in top right corner). This should help.
And fourth screenshot - "field notes are uploaded succesfully" - damn I again forgot. It's an issue because this feature should be only in Locus Pro