I’m afraid you set up your seedlings for a lethal race: There are so many seedlings per area, that they are trying to outcompete their neighbors in search of space, light and nutrition by stretching as long as they can. Looking at the window box, that’s even worse - for them, the high sides is like being at the bottom of a deep valley.
Next time, be a bit more light-handed and use a lot less seed, off the cuff, I’d say a fifth should be plenty.
For the existing batch, you can either wait and see how many will succeed and watch them self-regulate, but they will get even lankier and them being so crowded increases the risk of e.g. fungal infections, which can at worst cost you the whole lot. Instead, gently pull out the majority of the seedlings, disturbing the remaining ones as little as possible. If necessary, cut or pinch them off right at the soil surface. If you can manage to raise the ones in the window box, that would also be good, but it’s probably not feasible - and at the current state with just the cotyledons they are too young to be transplanted.
The grass clippings don’t help at all, at worst they can harbor disease or feed fungi, that could move on to the seedlings.