The operation can’t be completed because the original item for “LaCie M1” can’t be found.

Give smbd Full Disk Access. It may already be in the list in Privacy & Security System Prefs, but you have to enable it.

If not, I don’t remember where it is. I won’t be able to poke around until tomorrow.

Sounds like the alias has lost track of its original item.

Is this in the SideBar or Dock? Both of those store aliases to the original, so you may have to remove the entry and add a new one. To remove it from either, click and drag it out until you get a "remove" or "x" popup. Let go.

You can find the drive by using Go > Computer in the Finder (cmd-shift-C).

Drag the drive icon into the Sidebar or Dock as desired.

I guess I don't understand where it goes missing.

Are you trying to open it on the host computer (the one it is directly connected) or from a networked computer?

If it is the host computer, does it open fine with Go > Computer?