If the user already exists the email will be a warning + a link to the password reset form
If the user does not exist, the email will be a link that confirms the ownership of the email address and the rest of the registration process.
An attacker trying to guess if an email is registered would not know, because the form does not give away that info.
I know that there should be some kind of compromise since any security measure added to secure accounts will lead to some inconvenience for users.
If your goal to make sign in process as smooth for users as possible you may want introduce as little steps as possible between their landing on a page and "purchase".
But verification of email address should be kind of mandatory and happen before something important will be sent to this email.
As soon as you find a valid login, you can test all known passwords (plus variations) associated with it.
But since you are giving advice to the DESIGNER of the site, why not simply tell them not to use passwords? https://qbix.com/blog for example
It's a tradeoff between usability and security, and each site should make their own decision about what is right for them.
It obviously makes attacks like the one in the article easier, but there are other ways to mitigate that.
An example often given for when revealing an email is registered would definitely be bad is dating website and pornography websites - where identifying someone is a member alone could be embarrassing or compromising.
Outside of such scenarios, websites may decide the increased conversion from a more streamlined registration process and lower numbers of support requests for login issues outweigh the marginal security gains from hiding that information.
How will the user know that the registration failed and what to do about it?