Dow Corning also makes fiber glass that is snow white. Pillow cushions have floss fill in them also. If you've been in the business very long you would have done a burn test to narrow down quickly the identity of this fluff. glass or asbestos won't melt using a lighter.
Being a 2004 built house it's pretty unlikely to be asbestos, unless you live in a country that still uses it in carpet manufacturing. In the USA it hasn't been used in about 30 years.
The pictures just show some kind of fluff which could be lint, or as mentioned hair from pets. Keep in mind that not having a pet now doesn't mean there have never been pets in the house.
If you're worried about it, skip the dry vac, prespray and HWE. As long as it's wet no asbestos fibers will go released into the air. They stick together wet. When you're done, rinse out your wand and hoses before they have a chance to dry out, and drain and rinse your waste tank into a sewer system. Even if that is asbestos carpet, you're not going to remove enough fibers to be of any concern.