My trust in such a brand quickly goes to zero.
Take this random Brandless product: https://brandless.com/products/stainless-steel-wooden-turner
Why on Earth would you buy it? How can you possibly tell that it's eco-friendly or not?
I looked at a lotion, which includes the ingredient "fragrance". This is automatically questionable because it doesn't tell you what the ingredient actually is. Moreover, it's a term that companies use instead of telling us what's actually in the product, including any number of potentially harmful ingredients. It is also patently not required for the product to function, so it's clearly against Brandless's stated aim.
Brandless looks to me like an Orwellian marketing gimmick: they claim to be brandless, yet they're actually trying to develop a brand.
Edit: A bit of poking around suggests that Acacia is a fairly sustainable source of wood, so I would guess that's the thing that makes it eco-friendly. Some of their other acacia products do mention this, but the spoon doesn't for some reason.
I do wonder why they felt the need to add metal at all though; I’ve never felt that a plain wooden spoon was lacking anything and having a heat-conductive material in a hot pot seems like a good way to get a burn. The description just says it’s a “nice accent.”