This has been exposed via the metadata API documented here
ProfileActionOverride
Represents an override of an ActionOverride by a user profile. You can use it to override an ActionOverride on a standard Home tab or object record page in Lightning Experience. When a user logs in with a profile, a matching ProfileActionOverride assignment takes precedence over existing overrides for the Home tab or record page specified in ActionOverride. You can only access ProfileActionOverride by accessing its encompassing CustomApplication or Profile. Available in API version 39.0 and later.
Metadata XML Sample
<CustomApplication xmlns="http://soap.sforce.com/2006/04/metadata">
<profileActionOverrides>
<actionName>View</actionName>
<content>CustomObjectFlexiPage</content>
<formFactor>Large</formFactor>
<pageOrSobjectType>TestObj__c</pageOrSobjectType>
<type>Flexipage</type>
<profile>standard</profile>
<recordType>TestObj__c.TestRecordType</recordType>
</profileActionOverrides>
<defaultLandingTab>standard-home</defaultLandingTab>
<formFactors>Large</formFactors>
<label>My Custom App</label>
<tab>standard-Account</tab>
<tab>standard-Opportunity</tab>
<uiType>Lightning</uiType>
<navType>Standard</navType>
</CustomApplication>
Package.xml
<?xml version="1.0" encoding="UTF-8"?>
<Package xmlns="http://soap.sforce.com/2006/04/metadata">
<types>
<members>MyCustomApp</members>
<name>CustomApplication</name>
</types>
<version>39.0</version>
</Package>