"Soup" is a good word. Pieces of DNA resulting from destruction by nucleases and other enzymes.

> This always blows my mind. We are currently breathing in the DNA of the trees,

At this time of year, believe me, I am aware of the inhaled tree DNA setting off my pollen allergies.

The immune system destroy all the DNA in unexpected places in case it's a https://en.wikipedia.org/wiki/Viroid or something. Better safe than sorry.

One of the important steps in mRNA vaccines was to surround the mRNA with a lipid to ensure it can survive long enough to enter a cell. Naked mRNA would not have worked.