I have experienced this sticky drag-and-drop bug over many Ubuntu versions, currently 20.04, but it seems to be very old (see launchpad). If you have a touchscreen or tablet it is very likely to be involved in the bug. If so, you should be able to temporarily fix by hitting ESC to get your mouse pointer back, then sometimes, just using your touchscreen (or whatever is involved, e.g. tablet, etc) instead of your mouse to click the offending feature clears the problem (until the next time).
Sometimes it doesn't. Then, open a terminal with CTRL+ALT+T, then type
xinput at a command line to find the id of your touchscreen/tablet. Then, if it's 12 for example, type:
xinput --disable 12
xinput --enable 12
If that doesn't work, try using your mouse between the disable and enable commands. If it's not obvious which device ID is which, try a process of elimination. For example on my Lenovo Yoga 3 Pro laptop:
⎡ Virtual core pointer id=2 [master pointer (3)]
⎜ ↳ Virtual core XTEST pointer id=4 [slave pointer (2)]
⎜ ↳ Synaptics TM2714-001 id=11 [slave pointer (2)]
⎜ ↳ ATML1000:00 03EB:8A10 id=12 [slave pointer (2)]
⎜ ↳ PixArt USB Optical Mouse id=14 [slave pointer (2)]
Most people notice the bug when every click on a nautilus bookmark puts the system into drag-and-drop mode. For me, another repeatable symptom affects LibreOffice Calc. Once the bug has been triggered, if you click-select a worksheet tab or drag-select a set of cells then release the mouse, it also becomes stuck in drag-and-drop mode, and (strangely) draws a thick border around the selection, which you cannot undo or reformat.
sudo journalctl -f?