Accidentally bought a game that I already have in my PS+ Essential library. If I refund it will I lose my PS+ copy?

Was buying Helldivers 2 today and accidentally also bought FF7 Remake due to it being in my cart from a while back. But I already have it on PS+ Essential, and also a physical copy so I'm going through the refund process now.

But my question is, will I lose access to my PS+ copy if they refund it? Logically it seems like I wouldn't but I'm curious if anyone has experience with this since I don't trust the chat agents to know everything.