I think you'll see CBDC's and Crypto both learning from each other in some sense. Basically as a digital (Fiat) currency, the monetary policy surrounding it can be programmed - which could make it more like crypto in that it could derive it's authority from a sound programmable policy rather than by "decree".

Also, with world wide currencies that are exchanged between nations, there should be layers of privacy protection built in or no one will use it - of course those solutions would have to come from Crypto communities. Perhaps the digital networks that trade CBDCs could utilize zero knowledge proofs, Secure Multi Party Computation - things like that.

Things like GDPR compliance rules in websites coming up against KYC regulations means that doing business with digital money in web3 apps might mean you need to prove you are who you say you are to a company without them having the liability of actually collecting and storing your data.

I don't think anyone can completely discount the power that government backing can have with Fiat - but hopefully Crypto can engineer solutions for CBDCs to exist with Crypto in a world economy and give some privacy and anonymity.