I'm on a Mac and its harder to connect my Galaxy S22 to it, using either Android File Transfer or OpenMTP. I use a Windows VM on Parallels to do so. Either way it always asks for permission to connect on my S22, which can get in the way of connecting. It can show up on Windows, then disconnects and asks for permission. It may or may not show up for real afterwards, which can be pretty annoying.
Based on your description of your environment, you have three different connections that your phone has to deal with:
Connection 1: Your Mac (bare metal)
Connection 2: Parallels (hypervisor)
Connection 3: Windows VM (virtual)
Your S22 sees it as three separate, sequential connections. Which means you need to give permission for each separate connection. When your S22 asks for permission to allow the connection, does it give you an option to not ask again? If so, tell it to not ask again. You will need to do that for each connection. However, if your connection environment changes (i.e. your VM is assigned a different ID from Parallels.), you will need to do it again.
You will also need to ensure that your Mac and Parallels are allowing the connection without prompting. I don't know enough about Mac and Parallels to walk through that piece. Turning on USB Debugging will have no affect in this.
If it is dropping the connection, it may be either your physical connection disconnecting (Mac), or the hypervisor (Parallels) disconnecting. Also, the phone will also disconnect after a certain period of idle time. This can occur if you are copying large amounts of data.