How does that answer my question, how do NFTs help an organization prove that a key belongs to them?

NFTs and blockchains are an entirely virtual construct that can't affect the real world, or take trusted, non-key inputs from the real world. That's not 100% true, but it is mostly true.

So really, you need a way to tie or bind a key to an identity or organization. You could perhaps sign some data, such as a domain name with a key on a chain, but that doesn't prove anything. Anyone could sign anything with any key, so you need to approach the problem from the other direction.

You can install the key directly, or the hash of the key into DNS, verifiers can retrieve the key from DNS, then resolve it to the full key if necessary. You can then use the key to verify signatures of signed data.

Why DNS? Because that is currently the most standard way to identify organizations on the internet. Also, much of the security of the internet is directly bound to DNS. For example, getting certificates for websites often entails changing a DNS record at the request of an issuer to prove that you own the domain in question.

This is not an idea I invented just now, there are multiple DNS record types that have been defined for literally decades at this point which allow an organization to publish keys to DNS. Among the first is this: https://www.rfc-editor.org/rfc/rfc2535#section-3 Not completely related, but it is a key of some kind published to DNS.

I don't think NFTs provide any useful functionality in helping organizations prove that a key is theirs, at least nothing much better than a simpler solution which already exists.