Can I create a Sub-Domain with email with seperate DNS settings?

I have a primary domain, livinre.com, for my website, and I am using Gmail for sending/receiving mail from tyson@livinre.com.

I also have a 3rd party contact management system for sending bulk and auto emails. I need a separate email with separate DNS settings for that to work, as I can only have one sending/receiving email service in DNS settings.

Is it possible to set up a subdomain/email, like tyson@alerts.livinre.com with separate DNS settings to use in this 3rd party system?

I have already tried to set up an alias and a secondary domain through Google Workspace as pictured/attached, but I do not see that I have separate DNS settings anywhere for those.

If this is not possible, I will purchase a whole new domain, like alertslivinre.com, that I can manage separately. Exploring options before I do that.