Yes, Zoho Mail and ZeptoMail are two different services and hence require separate domain verification. Even if you're using the same domain, you will have to verify it separately in both services. It is mandatory to verify your domain to ensure good deliverability of your emails.
While you can use the same domain in Zoho Mail and ZeptoMail, it is advisable to use a dedicated subdomain for your transactional email sending. Specifically to isolate it from your marketing emails. It is recommended to have a separate subdomain to send transactional emails to improve your sender reputation and boost your domain's credibility.