When using the inventorio inventory on a server, I cannot move items in the inventory, as they move back to where they were before, unless I shift click
I own the server and everything works fine in singleplayer

Video attached incase I phrased it poorly (sorry about weird aspect ratio)

I see you are using Minecraft 1.19.2. I no longer support that version and I can't reproduce that issue with 1.20.4. So I'll close this, but feel free to re-open it if you encounter the same issue in any 1.20 version.