Your request is an interesting one: I agree it would be good if we had a way to really turn off truncation altogether for testing purposes, even if it led to exactly zero singular values (because then you can definitely look).
Let me comment on your setup first, though, then please let me know if you'd still like the "no truncating" feature.
From your initial state and the operator you've defined, I'm pretty sure what is happening is that one of the terms in your operator, when acting on a bond (j,j+1) is just flipping the two neighboring spins and the other is just evaluating to zero. That's if the spins are different. If they are the same then that term just gives zero.
So then I'm pretty sure your operator is just always mapping product states to product states and that's why the bond dimension doesn't grow (& I'm surprised it grows even to 2 and not just stays 1).
Finally, you can be assured that if the bond dimension doesn't grow, it's because the singular values really were zero or else below your cutoff (more precisely their sum was below the cutoff). So they must be smaller than 1E-15.
But if you think the feature of no truncation would still be helpful, it might not be too hard for us to add that.