Workflow / Tool to count cuts in footage material
You might want to try Algorithmia's Scene Detection. It detects timestamps where the algorithm assumes there is a cut. Then you just have to count the number of timestamps to get your result. You need to setup a Python environment for that and have some basic programming skills. I haven't tried it, so I cannot say how well it works.
Update:
Premiere Pro now has an edit point detection. It's quite new, at first glance the results look good. You may want to give it a try. To count the number of cuts, select &quot;Create Clip marker...&quot; in the dialogue and export the markers to a csv file.
Pretty much all solutions can be inaccurate to a certain degree. Some methods of cutting are hard to detect, like match cuts or invisible cuts. Be aware that some of the found cuts might not be cuts after all but are other types of transitions, like dissolves or morphs.