The issue started after the September updates, specifically KB5122882. I installed the out-of-band (OOB) update (KB5129237) released by Microsoft to address the issue

What finally worked: disabling WDDM for RDP
The workaround that resolved the issue in my environment was disabling the WDDM graphics display driver for Remote Desktop Connections through Local Group Policy.

Steps to reproduce the fix
Log in to the affected Windows Server locally or through an alternative management method.

Open gpedit.msc.

Navigate to: Computer Configuration > Administrative Templates > Windows Components > Remote Desktop Services > Remote Desktop Session Host > Remote Session Environment

Open Use WDDM graphics display driver for Remote Desktop Connections.

Set the policy to Disabled.

Apply the changes and reboot the server.

After the reboot, RDP started working without problems in my environment.