Do I need a crypto wallet to make an account?

まだ日本語では提供されていないため、原文で表示しています。上のメニューから翻訳できます。

No. An email address, or a Google or Apple account, is all it takes. Everything that does not touch the blockchain works without a wallet.

A wallet is something you connect to an account you already have, when you want to do something on-chain. It is not a way to sign in, and connecting one does not change how you sign in.