Does Edge share your browsing history with Microsoft?

Yes, also it's not even encrypted. It's the worst case of all major browsers.

Firefox & Safari: E2E encrypted, you hold keys, not possible for Mozilla/Apple to access it.

Chrome: Encrypted, Google holds keys meaning it is useless, they can read and give away the data. One can enable sync passphrase which would enable E2E however.

Edge: Nothing is encrypted and no way to change this.