Because you are using Snap. In that case see the FAQ for how to locate the directory. As for the path to Shotcut and melt, the snap should already include these in your path. Or, start looking in /snap ; it is clear and obvious from there.
Snap includes the following executables in your $PATH if things are setup normally (/snap/bin is in your $PATH): shotcut shotcut.ffmpeg shotcut.ffplay shotcut.ffprobe shotcut.glaxnimate shotcut.melt