Yummy, Seed Buffet!
Well, adding the straw makes it even more appealing for the chickens to dig to find what's underneath.
Depending on the germination requirements, you may be better off covering the seeds with loose soil that is not noticeably different from what you currently have (not potting soil, they love that). Then after a few rains, it will settle in and seem like part of the landscape.
I've learned firsthand not to dig holes or move planting media where my chickens can see. They always want to improve on my efforts.
Fencing around the planted area is a good idea from
@FernwoodHollow
And they will stay very interested in the new, tender shoots until it starts to mature. So you're looking at about a month or more of keeping them out of the area.
At least if you have portable fencing ready to go, you can move it around for the next bare patch.
I don't know where you're located... But if we weren't in the south, I really want to try planting Timothy. The blades get a lot wider, while still being a palatable soft grass, so I think it could potentially hold up to chicken traffic a lot better. But it's too hot for that here.
In general, best to stick with grasses that can grow vigorously in your area / season. Pasture mixes can sometimes do better, depending what's in it.