FINALLY FIGURED IT OUT!!!!
God, Apple, y'all could make this easier!!! In Windows you "Map a network drive" and then there's a checkbox that says "restore mapped drive on login." EASY PEASY. But, NOOOOOOO, you have to be DIFFICULT!!!
I love my Mac, but y'all make some STUPID DECISIONS sometimes!! (Don't get me started on how y'all RESET all the default programs every single time I have to update MacOS!!! Talk about a STUPID DECISION!!!)
Anyway -- here's how to do it:
-- Open Script Editor
-- Paste the following code into the Script window:
delay 15
do shell script "open smb://username:password@servername/sharedfolder"
(obviously, change the username, password, servername, and sharedfolder to match your setup.)
-- Run it first by pressing the "play" button at the top of the Script Editor window. Gotta make sure it works before you save it.
-- Save it as an Application (NOT as a Script!!) to your Applications folder. Call it whatever you want. I call mine "MountShareDrive" (no spaces). I highly recommend you *don't* use spaces, because if you ever need to use this app in a script, you'll regret having spaces in the name.
-- In System Settings | General | Login Items, click on the + in the Open At Login list and browse to your Applications folder. Double-click on your newly-created application to add it to your Login Items list.
Next time you reboot, it'll login to your network share 15 seconds after you log in. The "delay 15" line is what finally fixed my problem. The Mac apparently takes a few seconds to query the network as to the names of all the local devices it can see. Simply having the "open smb://blah-blah-blah" command with no delay will cause it to fail (as it was failing for me) with a "cannot find 'servername'" error. (And, of course, as soon as I manually ran that "open smb://blah-blah-blah" command, it'd work fine. Because it had been long enough since login for the Mac to know the names of the local devices.). If you still get "server unknown" errors, just increase the delay. Maybe your network (or the shared devices) are slower to respond than mine are. And of course, make sure you can actually connect to the device manually, before you try to do this via a login script.
Again, Apple, y'all could make this A LOT EASIER!!! Ridiculous!!!! MacOS is supposed to be the BETTER alternative to Windows. This kind of stuff *REALLY* makes Windows look better. Ugh! I'm an advanced user and it took me TWO DAYS to figure it out. UNACCEPTABLE!!!!