I have a custom domain for my emails with catch all. When I create an account somewhere I just use <name of the service>@my-domain.com

Can I find out if any of my emails are in leaks with a service somewhere?

That's literally what Have I Been Pwned is for.

One by one, but I think the question is about the entire domain name

	▲	Brajeshwar 2 hours ago \| parent \| next [-]
		You can have haveibeenpwned.com check for the custom domain itself. For instance, I get notified if any email of our family domain get leaked (not just mine).
	▲	wongarsu an hour ago \| parent \| prev [-]
		If you sign in that's an option on your dashboard. You need an account because you need to verify the domain is yours