macOS Monterey has been known to introduce compatibility issues with various external devices. If it was working fine before with macOS Monterey, then perhaps a macOS update has created a compatibility issue. Was this SSD ever working with Monterey before?
What file system is used on the external SSD?
Is it encrypted?
Are you using any third party software to manage the SSD? If so, then that third party software may need to be updated to work with macOS 12.4. You may need to contact LaCie for assistance.
When there was some compatibility issues before with external drives, some users found that using the Apple USB-C charging cable allowed them to access their external drives (no lightning bolt icon on the connector), but transfer rates were extremely slow because the Apple USB-C charging cable only operates at USB2 speeds. Normally you want to use a Thunderbolt 3/4 USB-C cable which includes a lightning bolt symbol on the connector to use with your external drives.
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https://www.apple.com/shop/product/MN713AM/A/thunderbolt-4-pro-cable-18-m
Try disconnecting all other external devices in case one of them is causing a problem or compatibility issue. Wacom tablets were one such device which has been known to cause issues with external drives.
Connect the drive directly to the Mac. Make sure to try a different port especially on the other side of the laptop if one is available.
Try running Disk Utility First Aid on the hidden Container on the SSD. Within Disk Utility you may need to click "View" and select "Show All Devices" so that the hidden Container appears on the left pane of Disk Utility. Even if First Aid says everything is "Ok", click "Show Details" and scroll back through the report to see if any unfixed errors are listed. If you are using the APFS file system on the SSD and there are unfixed errors listed, then you will need to temporarily transfer the data to another location in order to completely erase the whole physical drive to resolve the file system issue. You may also want to run First Aid on the physical SSD too to check the integrity of the partition table (the physical drive will usually be identified by the make & model of the drive or the USB chipset used in the drive or adapter/dock/hub).
It is also possible the laptop is not providing enough power to the SSD. Maybe try using a dedicated power supply for the SSD or try using a powered USB3 hub.
What is the exact model of the Mac where this SSD is not working? You can get this information by clicking the Apple menu and selecting "About This Device".