I would probably resin coat my floor instead of using urethane, but I would agree there. Even concrete floor contains silicates. I also wonder what kind of microparticles scuff off of a tile floor.

Shellac or traditional varnish are probably the only things you could put on your floor that aren't produced with an industrial process. Shellac in particular is the harvested secretions of a beetle that have been cleaned and dissolved in alcohol. But it's water-soluble and so probably not appropriate for use on a wood floor. You could also use tung oil or boiled linseed oil but you'd have to sand down to #0000 steel wool to get it to shine like urethane. Tung oil is a nice coating because it doesn't turn orange like BLO, but either one you will have to keep applying every few years or the floor will stop repelling water.

Obviously we'd end up with huge Tung plantations or Shellac plantations if we tried to replace all of our floor coverings with this stuff.

To my knowledge, olefin synthetic carpet is not known to contain phthalates. I would however avoid the ones that claim to be stain-resistant, as they're more likely to contain iffy coatings.

Carpets often repel water… using PFAS.

Yeah, and I bet even the expensive wool stuff that only rich people buy is treated with scotch guard and flame retardants with questionable health effects.