You cannot deploy 'EmailServicesAddress' independently, they would be part of 'EmailServicesFunction'. Use VS code or Workbench and you should be able to successfully deploy Email Addresses. Was able to do successfully using workbench.
Package.xml
<?xml version="1.0" encoding="UTF-8"?>
<Package xmlns="http://soap.sforce.com/2006/04/metadata">
<types>
<members>Emailservice</members>
<name>EmailServicesFunction</name>
</types>
<version>50</version>
</Package>
Metadata
<?xml version="1.0" encoding="UTF-8"?>
<EmailServicesFunction xmlns="http://soap.sforce.com/2006/04/metadata">
<apexClass>myHandler</apexClass>
<attachmentOption>None</attachmentOption>
<authenticationFailureAction>Discard</authenticationFailureAction>
<authorizationFailureAction>Discard</authorizationFailureAction>
<emailServicesAddresses>
<authorizedSenders>[email protected]</authorizedSenders>
<developerName>Emailservice</developerName>
<isActive>true</isActive>
<localPart>testing</localPart>
<runAsUser>[email protected]</runAsUser>
</emailServicesAddresses>
<functionInactiveAction>Discard</functionInactiveAction>
<functionName>EmailTest</functionName>
<isActive>false</isActive>
<isAuthenticationRequired>false</isAuthenticationRequired>
<isErrorRoutingEnabled>false</isErrorRoutingEnabled>
<isTextAttachmentsAsBinary>false</isTextAttachmentsAsBinary>
<isTlsRequired>false</isTlsRequired>
<overLimitAction>Discard</overLimitAction>
</EmailServicesFunction>
Please note 'EmailDomainName' is a read-only field and the system generates a unique domain part for each email service address to ensure that no two email service addresses are identical.
Also, check limitations of standard object(Email Services Address) here.
Thanks