Is applying for other positions during the early stages of a PhD you don't like considered bad?
Identifying that you are not happy where you are, honestly attempting to address the reasons and then, if you are still not satisfied, making the decision to leave before you become depressed and wholly negative, is far from unprofessional. Quite the opposite, in fact.
There should be no negative associations from taking a purposeful step away from an unfulfilling working relationship. For that reason, there is no problem for asking for additional recommendation letters from your referees for a different PhD position. They might be curious why the previous position didn't last. Being honest and professional with your reasons is a good policy.
You mention that you are &quot;employed in a test phase&quot; for a few months. Does this mean that you are in some kind of provisional stage of your PhD programme? It is not uncommon for PhD programmes to have some kind of initial provisional period during which both the PhD candidate and their supervisors develop their working relationship. If by the end of the provisional period it emerges that the PhD candidate and the supervision team are a poor fit to each other and/or to the research programme, the PhD registration can be terminated and everyone goes their separate ways.
There is no downside to this, despite many candidates viewing this as &quot;quitting&quot; or feeling that they were at some kind of fault for not making it work. The PhD -- supervisor relationship is just that: a relationship. In addition, there are occasions where it becomes obvious that the research project and/or student and/or supervisor are a poor combination. Normally this would have been avoided during an initial registration period, but sometimes the disconnect(s) are only discovered later in the piece.