Does the IKEA Besta series back panel lack stability?

Weren't there any nails included to nail the back panel to the sides, if the back panel remains movable in the grooves, it will never be stable

The back panel is no longer nailed - it is only slid into the corresponding groove. Attached is also a picture from the assembly instructions.

what kind of strap would you take?

For example, a piece of a tie-down strap or similar.

You could also use a lath and then nail it into the side panels. You can find that at the hardware store. My recommendation: Either attach it to the wall after all or even better return it and switch to Metod. Besta is basically recycled paper with paint (and I have Besta myself). Metod is still reasonably stable.

Am I blind? How much does it shift to the side? I don't know Besta at all to act like a diva.

Then use the solution with the band

You mean the pivot band, or wall band? But that's not for angular adjustment. I would also temporary nail the wall at the back. Align angularly beforehand.

switch to Metod. is basically trash

That's right. I now also have Metod sideboards.

You mean the strap hinge, that is wall strap?

No, I mean a sufficiently long non-stretching strap to modify the thing craftily so that it works. Nothing from the scope of delivery.

There is also this support cross for shelves, with that you also get stability for the cabinet