Bizarre mushroom / fungus growth
Disclaimer: in providing this identification information I am not making any claims about its edibility or lack of edibility.
The fungus in the photos appears to be one of a group commonly known as a puffball. They are likely growing on the wood mulch that you applied. They probably emerged in such large numbers because of the recent extended periods of rainfall. If you cut these mushrooms open you will find either a solid mass or if it is more mature, a powdery mass of spores. There is also a chance that the fungus in the photos isn't a puffball, in which case you would see the outline of a developing mushroom inside. https://www.mushroomexpert.com/puffballs.html Look at this website for more photos for comparison, and to get a better idea of what is actually involved in identifying a mushroom. to be sure of identification, it takes for than a couple of photos. https://www.mushroomexpert.com/lycoperdon_pyriforme.html
As to the second part of your question- how can you get rid of them? You can't do so easily. The fruiting bodies or mushrooms can be removed and bagged up and disposed of, but the more hidden part of the fungus, the mycelium, remains waiting to produce more mushrooms when the next rainfall comes, and conditions are right.