But it's not seeing what domains are associated with your email; rather, it's seeing which emails for a given domain (e.g. a company domain) are associated with breaches. If you can demonstrate that you have control over a particular domain, then haveibeenpwned will tell you how many (and maybe which?) accounts on your domain are compromised. If there are more than 10 such accounts, it looks like you need a paid subscription.
But it's not seeing what domains are associated with your email; rather, it's seeing which emails for a given domain (e.g. a company domain) are associated with breaches. If you can demonstrate that you have control over a particular domain, then haveibeenpwned will tell you how many (and maybe which?) accounts on your domain are compromised. If there are more than 10 such accounts, it looks like you need a paid subscription.