I tried to disable this via the Windows Registry, as some other features can be disabled. I navigated to version R24.1 > ACAD-5101:409>Applications>CloudAccess and changed "CloudAccess" to "CloudAccessOFF". While this works for other things, in this case AutoCAD just created a new "CloudAccess" key. That is probably why it still shows up even after you uninstalled it. It seems something in the programming is reinstalling it every time the program loads if it can't find it.
Fortunately for me, I don't see the Share button because I have a floating Layers toolbar in that location that covers it up.
Work: AutoCAD 2022.1.3, Windows 10 Pro v22H2 64-bit, Intel Core i7-8700K, 32GB RAM, Samsung 960 Pro SSD, AMD Radeon Pro WX 5100, 3 Dell Monitors (3840x2160)
Home: AutoCAD 2022.1.3, Windows 10 Pro v22H2 64-bit, Intel Core i7-11700, 64GB RAM, Samsung 980 Pro SSD, NVIDIA Quadro P2200, Dell Monitor (3840x2160)