Here is a post that gives you an indication of how worn your chain is. Basically, look at how high up the square box that is the latching mechanism is.
Turning the crank backwards a bit is of no consequence, so long as you always turn it back the right way and tension in up again. From a cam/crank point of view, a slack chain tensioner will mean that the cam and crank will go slightly out of sync to each other, but since you are not running the engine, you aren’t going to do any valve damage delicately turning the engine by hand a few degrees and you’ll reestablish the cam/crank relationship as soon as you turn the engine the right way again. From a tensioner point of view, you want the tensioner to always be pushing the slack chain to the middle of the block rather than being loose where it can snag on something - that’s your concern.
The worn chain in the picture cuts into a couple of the bolts into the engine block - there is metal to metal contact.
The straighter the tensioner is, the more tension it is applying to the chain.
A tensioner that doesn’t tension is just going to whip about and will cut grooves into the plastic tensioner and chain guides in normal operation. If it is maintains proper tension, then I can’t see why the engine can’t go backwards slowly by hand - there’d be nothing for chain to snag on and the cams and crank will still be sync’d to each other.
That also means that a worn chain will allow you to pull back and manipulate an unlatched tensioner quite easily as it isn’t under much tension if the chain sits a long way into the centre line of the block. By contrast, a new chain will keep the tensioner sitting to the right hand side of the car and under heavy tension by default so there is little or no scope to allow for lateral movement.
The tensioner sits on a pin coming out of the block which you have identified - it can’t go anywhere and you also can’t change it without removing the timing cover.
You do sound as though you are describing a reasonably worn chain, so check how high up the latching mechanism sits.
kind regards
Marek