Thanks for posting your question in the Microsoft Q&A forum.
According to your description, I will answer them in order:
1. Are shared mailboxes supported with HMA?
Shared mailboxes in Exchange 2019 support Modern Authentication (HMA). You can enable HMA for shared mailboxes to enhance security.
2.Do applications that need to connect to Exchange through EWS to send emails have to support modern authentication? What should be done if an application does not support modern authentication? Is there a workaround available?
I am a little confused about this question?
Is your environment hybrid? If it is a hybrid environment, you can only use Hybrid Modern Authentication instead of Modern Authentication.
Here is the official evidence from Microsoft: Enable Modern Auth in Exchange Server on-premises | Microsoft Learn
If you're using Exchange 2019 only, any application that needs to connect to Exchange via EWS to send mail must support Modern Authentication.
If your application doesn't support modern authentication, you can either change the application or use the Microsoft Graph API.
If my answer is helpful to you, please mark it as the answer so that other users can refer to it. Thank you for your support and understanding.
Best