SharePoint 2019 SSO Entra with OnPrem AD Account

I maintain a legacy SharePoint 2019 onprem installation. This installation has been around since 2007 and is wholly reliant on local AD accounts for access. We have a Microsoft 365 environment where our onprem AD Users are synced up to Entra.

We are in the process of making our onprem applications available through "My Apps" via the Microsoft Application Proxy.

My goal is to have a user login to My Apps and seamless login to the SharePoint 2019 environment.

I have followed this tutorial to setup the trust, which is working.  https://learn.microsoft.com/en-us/entra/identity/saas-apps/sharepoint-on-premises-tutorial

The issue that we are having is that the user being passed is not the onPrem AD user (slhilbert), but instead the Entra user (email address removed for privacy reasons).

The Entra user doesn't have any access setup in the SharePoint site, which has 100K unique permissions, is it possible to login with onPrem AD user?

Thank You!

Stuart