Web3 includes all of the previous web technologies and adds optional layers on top. It is a superset of all web tech. You can totally setup an HTTP server on a Raspberry Pi, that's totally still Web3, but good luck building a truly scalable multi-million user application and competing with AWS on that.
If your app is such that it relies on user-generated content, it wouldn't be Web3 for you to host it exclusively on your Pi, because the users generating the content would not own it, or have guarantees that the data on the Pi was not being manipulated or misused by you. The key idea of Web3 is user ownership and community ownership.
> With web3 there is gatekeeping and centralisation as I cannot spin up my own server any more without buying crypto and then paying someone on a centralised database just so that I can do everything I could do before for free on my own.
You can set up your stack however you like. You don't even have to be using cryptocurrency for payments to be "Web3". You could, for example, allow someone to login with their Ethereum wallet and use their ENS domain name as a username in your chat app rather than adding Google Auth. That doesn't even require a transaction on the blockchain, it's just verifying a cryptographic signature.