Pretty nice! I'm also trying to get ok results with plant milk and basic tools. You are totally right that the 'barista' version changes everything. Right now I'm using my roommate's frothing wand with terrible results :(. She's moving soon so I'll have to look into another option.
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Yeah, those frothing wands are terrible.
This is the French press I use: https://www.bodum.com/au/en/10948-01-brazil
Oat milk can be tricky. I've never tried French press frothing but I've heard it can give good results. Good luck!
I find oat milks labelled as "barista" are pretty good. The have some added fats I think, to make it creamier.
A french press is pretty handy for frothing. I've got a small Bodum with a plastic handle, so I can microwave the milk directly in the body of the press. Takes 50sec on high in the microwave, and I can pull a shot in parallel while it heats.