Shift right clicking the backpack on the ground picks it up, but immediately places it again, if the ground is reachable.

That definitely isn't the case with just SBP in the pack or in Enigmatica 6 pack that I play. Sounds like some kind of mod interaction issue.
Can you actually recreate with just SBP?

Collision is with mod PreciseBlockPlacing.

Is possilble to disable pick up the backpack by shift right click?
I can always pick it up by breaking it.
Btw, netherite backpack drops nothing!

I thought, to disable it only as an option, in config...

5 tick cooldown on pickup is included in the latest release that should take care of this issue.