Wood chips often work well (bigger pieces than shavings.)
Whatever you have that is free or cheap is a good starting point. So if you have dry leaves, I would start with them.
Straw tends to pack down into a muddy mat, then when it dries you have something hard like a brick. Wood shavings (thin little pieces) tend to disappear into the mud. Dry leaves tend to pack flat, similar to straw, but they don't interlock quite the same way. Bigger pieces of wood (wood chips, wood chip mulch, etc) tend to work better because they keep their own shape. Even if some sink into the mud, if you just keep adding more, you eventually end up with a dry surface on top. And the underneath layers seem not to stick together as badly as some other materials.
It is normal for chickens to scratch through everything and eat small pieces. Yes, some chickens overdo it, especially when something is new. But most chickens are fine, most of the time. Making sure they have a source of grit can help them process anything that makes it to their gizzards (won't prevent impacted crop, but will prevent impactions further down.)