We are using Azure Virtual Desktop in the exact same setup. We have 2 domain controllers on-premises with an company.local domain. In the cloud (Azure AD) we have a company.com domain. With AD Connect we sync all users from company.local to company.com. Also, it is possible in your on-premises AD to create a UPN suffix. Here you can configure the users to also use the company.com domain in your on-premises AD.
For more redundancy we also have 2 domain controllers in Azure to handle sign-in requests done by Azure Virtual Desktop.
When you have this configured your users will be able to use AVD with their synced Microsoft 365 account.