Quitting PhD program during a probationary period and applying for other programs
If you are in the middle of a "probationary period," then you should feel no qualms about having to apply elsewhere. You tried to make the current position work, but you feel it is not a good fit for you. That's the whole point of the period—it's a tryout for everyone!

Obviously, working somewhere for two months is not enough for someone to form a strong opinion of your true capabilities, so I would not ask your present advisor for the recommendations you need to look elsewhere.

As far as your supervisor goes, I wouldn't worry about it too much; after all, your advisor may also feel that this isn't the best situation, and may think ti better to go your separate ways than to continue. Again, you're in the probationary period, not halfway through a PhD, so the overall commitment of time and resources is not enough to really justify (much) anger or resentment on the part of the PI.