Can't buy DLC on Steam

I'll sapre you the details, but I don't own Elden Ring on my Steam account, it is shared to my main account by another account that I own, and I can't buy the DLC on an account that doesn't natively own the game. If I buy the DLC on the other account, will it be shared to my main one along with the game when using Library Sharing? Maybe this is the wrong place to ask this question, but I feel like it's relevant to Elden Ring right now as I'm probably not the only one with this issue.