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Yeah, that’s fair. I just buy powdered broth online, along with most ambient ingredients/foods, it’s cheaper and more accessible for me.
Now you need to get into making miso, that also gives you homemade soy sauce. Idk what we did to deserve soy, must have been something good.
I get powdered vegetable stock/broth which works well for me. Oat milk wouldn’t do much to thicken it, if you want it to be a little thicker you could add a little cornflour.
I never enjoyed any homemade oat milk, it always seems weirdly slimy to me. I buy soy milk in ambient cartons and it stays good more or less indefinitely on the shelf. Obviously when I open a carton of it I keep that refrigerated and use it within a couple of weeks.
Kinda not answering the question, but as a lazy disabled vegan if I want a big umami moment I will drink a cup of vegetable broth with MSG and maybe a splash of soy milk. Delivers a truckload of umami flavor, quick, easy, tasty