Most retail nut milk is actually mixed with a variety of gums and other texture enhancers.
Fresh, homemade oat milk is actually really easy to make by that process, but store-bought oat milk needs to have consistent flavor and texture/mouth-feel. So there is a bit more that goes into it.
This is also true of other non-dairy milks. That’s why I only use Trader Joe’s or Westsoy shelf-stable soy milk for making yogurt. No gums.