How to know what happens to NFTs in other marketplaces?

Hi all !
Let’s say a user lists an NFT simultaneously in two marketplaces, mine and, say, Opensea. Then the NFT gets sold in Opensea. I should be aware of that event so that I can remove the “buy now” button in my frontend, among other things. How can I do this?

I am not sure listing an nft on 2 marketplaces isn’t even possible, since you would have to approve 2 addresses for that id, while there can only be 1 approved address?

But you can set 2 marketplaces as operators right?
This is from the ERC721 code:
// Mapping from owner to operator approvals
mapping(address => mapping(address => bool)) private _operatorApprovals;

Oh I see. You would just have to check if your contract is still approved then when you load your page, this might be a pain for a lot of nfts, but I do not see any other way