Hide My Email is an awesome product, no doubt, but why the mention of Have I Been Pwned? Security through obscurity is not worth two cents. Use a password manager and generate your passwords.
My thought process was if you search your primary email, you'll quickly see all the breaches with that email. Using a different email per service reduces the surface area (lateral movement). Security through obscurity has nominal value, but the reduction in ability to correlate has a much higher value.