Can I Unlock The Fallout: New Vegas Steam Achievements If I Buy It Through Bethesda.Net?

According to Bethesda's FAQ, you are purchasing a key to activate the game via Steam.

"Pease note that a Steam account is required to activate any game key purchased on Bethesda.net.

However, you have confirmed this was not the case. You'll have to get in touch with technical support to either correct or refund it.

I have made contact with Bethesda customer support, and sadly, only the newer games (Skyrim and onward) give you a Steam key. Linking accounts only works for the Online games, like Fallout 76.

So to get a Steam key, I have to refund my copy from Bethesda.net, and buy it again on Steam.