Firstly, don’t over tighten anything to the point that it causes damage. Looking at your photos, it appears that your chain tension is adjusted using an eccentric bottom bracket rather than the rear wheel position within its forks. In fact, your rear wheel appears to sit in vertical dropouts which means there is no horizontal movement/adjustment to tension the chain. On this kind of bike, chain tension is achieved by loosening the nuts that clamp the bottom bracket within its eccentric, oversized enclosing shell, rotating the bottom bracket to a position that provides the desired chain tension and then retightening the clamping nuts to the recommended torque.
Is the chain actually pulling the rear wheel forward and out of the dropout or is it pulling the bottom bracket backwards in the shell, in either case causing the chain to become slack. From the photos, I can’t see how the rear wheel could be pulled forwards without coming out of the dropouts. Is your chain over-tensioned? I would recommend having a bit of slack on your chain, usually just enough to waggle it up and down a bit midway between chainring and sprocket. Often you will find that if you tension the chain to what appears satisfactory and then rotate the pedals, the chain can either be too tight or too slack at different positions of the pedals. So you need to ensure that the chain is not too tight in any position.