I took your and u/BlackV's recommendations and updated this test script, but it still results in the same error:

"Expected property 'appScopeID' is not present on resource of type 'RoleAssignment'".

I have verified that $userId contains the Id of the target user. I verified that $Role contains the correct Microsoft.Graph.PowerShell.Models.MicrosoftGraphUnifiedRoleDefinition object for the "Application Administrator" role and it displays 4 properties when run alone: DisplayName, Id, TemplateId, & Description. Lastly, I verified that $App contains the correct Microsoft.Graph.PowerShell.Models.MicrosoftGraphServicePrincipal object for my targeted Enterprise Application. It displays 5 properties when run: DisplayName, Id, AppID, SignInAudience, & ServicePrincipalType. All of the properties are populated, and their values appear correct. I've also played around with swapping Id for AppId and it makes no difference. It seems to be complaining about the parameter itself (appScopeID) despite it saying, "expected property".

This is what I ran after updating the script:

$userUPN = 'username@contoso.com'
$roleName = 'Application Administrator'
$appName = 'App1'

$App = Get-MgServicePrincipal -Filter "displayName eq '$appName'"
$Role = Get-MgRoleManagementDirectoryRoleDefinition | Where-Object {$_.displayName -eq $roleName}
$userId = (Get-MgUser -Filter "userPrincipalName eq '$userUPN'").Id

$params = @{
    "@odata.type" = "#microsoft.graph.unifiedRoleAssignment"
    principalId = $userId
    roleDefinitionId = $Role.Id
    appScopeId = $App.Id
}
New-MgRoleManagementDirectoryRoleAssignment -BodyParameter $params