"Moving the app" just moves small parts of it. They're not put in the directory, so looking at the card itself (when it's not in the phone) in a PC won't show the apps, just the space used by the pieces is marked as used (so the system won't write over those pieces).
When you copy the card to the PC, since the app pieces aren't in the card's directory, they're not copied. Then you formatted the card (which really doesn't format anything, but it does mark everything as unused), and copied files back to it (probably overwriting the pieces of apps). Yes, the links are in the phone, but the pieces of app they point to are on the card, so you can't move them on the card, and if you could "copy them to the PC", then copy them back to the card, they souldn't be in the same place, so the links would be pointing to other files or garbage.
The only way to do what you wanted to do is to move the apps back to internal storage, format the card, then "move the apps to the card" again. Which none of us recommend - for a number of reasons, this whole problem being just one small one. If the phone's internal storage is too small for all the apps you need installed at all times, use it temporarily until you can get a phone with more internal storage. Don't depend on it as a way of increasing the phone's storage.
(And if the piece moved id the same size as, or smaller than, a symbolic link takes, you're using more storage for that link by moving that piece. If the whole app is written that way - lots of very small pieces - moving the app leaves you with less free space than leaving it in internal storage. Adoptable storage [using the card as internal storage] solves some of the problems, but not all of them.)
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