Hello!  Based on what I can see, I suspect you're seeing signs of squirrel activity--either caching food or retrieving food previously cached.  These holes will be relatively shallow (no more than a couple inches)--if these are burrow entrances (which they do not appear to be in the photos) then it is not squirrels.

Squirrels can be problematic landscape nuisances to manage.  Exclusion is the gold standard for any wildlife, but squirrels are difficult to exclude from a yard and it's not practical to put a net over the entire lawn!  There's some evidence that capsaicin, the spicy compound in hot peppers, can deter them.  It is commercially available--just be sure to read and follow label instructions if you end up buying a capsaicin product, since there is risk to you the applicator as well.  It usually needs to be re-applied regularly to remain effective.

Since the squirrels are likely hiding food, another strategy can be to try to find what ready food source they're finding nearby and, if at all possible, eliminate it.  Bird feeders, pet bowls, etc can provide a steady stream of "treasures" for the squirrels to bury.

I hope this is helpful!

Cordially,

John

Good luck!