@Admin - Thomas Morel , Apologies for the delayed response. Yes, Reverse DNS is currently not supported for the Azure App Service and Application Gateway. You need to explicitly configure your VM PIP with 'ReverseFqdn' property to enable it.
Note: Configuring reverse DNS for a Public IP address resource is currently not supported in the Azure portal.
$pip = Get-AzPublicIpAddress -Name "PublicIp" -ResourceGroupName "MyResourceGroup"
$pip.DnsSettings = New-Object -TypeName "Microsoft.Azure.Commands.Network.Models.PSPublicIpAddressDnsSettings"
$pip.DnsSettings.DomainNameLabel = "contosoapp1"
$pip.DnsSettings.ReverseFqdn = "contosoapp1.westus.cloudapp.azure.com."
Set-AzPublicIpAddress -PublicIpAddress $pip
Ref: https://learn.microsoft.com/en-us/azure/dns/dns-reverse-dns-for-azure-services