This is a classic issue when moving an older operating system like Windows Server 2003 R2 to a modern Hyper-V host, and you've correctly diagnosed the root cause: the new hypervisor presents synthetic storage and network controllers that lack native drivers in the 2003 kernel.
The most reliable path forward is to ensure the guest OS is prepared for the new virtual environment before the final migration. Since the original physical server is likely unavailable, you will need to take an intermediate step. First, create a Generation 1 VM on your Hyper-V 2022 host and attach the VHDX you created. Before booting it, you must add a Legacy Network Adapter and, crucially, change the SCSI controller to an IDE Controller for the boot disk, as Server 2003 has built-in drivers for these emulated devices.
Once you can boot the VM and access the network, the next critical step is to integrate the new drivers. You will need to install the Hyper-V Integration Services specific to older Windows versions. Mount the "vmguest.iso" from your Hyper-V host's resources (typically found in C:\Windows\System32\) within the VM and run the setup. This will provide the necessary drivers for the synthetic devices, allowing you to reconfigure the VM to use a standard SCSI controller and a modern network adapter for much better performance.
This process should stabilize your VM. I hope this step-by-step guidance helps you successfully complete the migration. If this answer resolves the problem for you, please feel free to mark it as "Accepted" 🙂