It seems like your version of elementary OS is based on an older version of Ubuntu. Unfortunately, the kernel of that version used to be compatible with the 340 driver, but it’s no longer the case. That’s why you can’t find it in the Ubuntu 24.04 repositories.
However, there might be a workaround for you. You could try installing the 340 driver from this PPA by following the instructions provided. But please keep in mind that there’s no guarantee it will work:
I know it can be frustrating when hardware becomes obsolete, and sometimes there’s no way around it.