The administration and maintenance of Microsoft Exchange Server to ensure secure, reliable, and efficient email and collaboration services across an organization.
According to your information above, you have a Headquarter domain and country domain in your environment, and you want to migrate the users in country domain to o365 without migrating the Headquarter domain.
If so, you will deploy a hybrid environment, for the mailflow in hybrid, we could refer to the official document Transport routing in Exchange hybrid deployments
If your MX record points to EOP, you will need to enable the centralized mail transport, so the messages will all be routed to the on-premises Exchange server
If your MX record points to the on-premises organization, the message is delivered to an on-premises Exchange server
And the domain suffix changing in Exchange hybrid, refer to the steps in this link: add-a-new-domain-to-an-existing-hybrid-exchange-configuration
For more information about deploying Exchange hybrid Exchange Server hybrid deployments and Use the Microsoft 365 and Office 365 mail migration advisor