There are various reasons that may cause your Lacie external hard drive to disconnect from your M1 Mac, such as disk sleep issues, damaged ports or cables, operating system bugs, insufficient power supply, outdated driver, third-party software interference, etc.
I see that you've tried to troubleshoot the issue by using different ports and cables and adjusting the battery sleep settings. To stop the "Disk Not Ejected Properly" message from recurring, here's what I recommend you do next:
Try using your Lacie drive with a powered USB hub: Chances are that the USB port on your Mac isn't providing enough voltage for your drive to work correctly. You can ensure it's receiving enough power by connecting with a powered hub.
Set the default disk sleep time to maximum: You can prevent your external hard disk from sleeping to avoid it disconnecting from your Mac. Open Terminal and run the following command in order.
sudo pmset -gsudo pmset -a disksleep 1410065408
Format the drive: If the message "Disk Not Ejected Properly" keeps showing up, consider backing up data on your drive and reformating it. If you can't access the drive, recover your data with iBoysoft Data Recovery for Mac first.
It'll find the inaccessible data on your external hard drive and allow you to preview them for free. Click the button below to download it for free.
If you'd like to learn about the details of the above solution or other solutions, check out the following guide: