NirSoft HashMyFiles can be controlled by a script [
Command-Line Options are described about three-quarters of the way down the webpage].
Perhaps it might suit your needs.
I am already familiar with it, and have been using various useful tools from NirSoft since the Win XP days, but I don't use HashMyFiles because both FastCopy and FcHash (the latter comes included with FastCopy as a separate tool) are similar to it. Thanks anyway for suggesting it. But, FastCopy gives the advantage of letting me copy my files in such a way that these same files don't need to be read a second time to calculate the file hashes.
That is, FastCopy gives the option to let file hashes be written to the log file that it can output
during the copying task. It supports both unicode and long paths, and it works well─better than any other copy tool that I have tried. FastCopy can either be used in CLI mode or be used in GUI mode, similar to WinRAR.exe and 7z.exe (the main difference being that it's just a copy tool so it can't create/modify/extract/test/repair archives). Parsing of the log files can easily be done by writing your own scripts.
One advantage of copying files on an NTFS volume in lieu of storing them inside ZIP/RAR archives is that files can immediately be used with the full featureset of NTFS so it totally eliminates the extra burden or need to extract files from archives. So, by simply hotswapping removable drives (be it via USB or via caddies/sleds/whatever), as a result of this it becomes possible to quickly conveniently switch back and forth the purpose/role of multiple individual drives between 'reliable backup copy' and 'currently actively in use', as I can physically unplug a drive and move it to a safe location before moving another drive away from the safe location (and plugging this other drive in). No need to do anything else.
For this same reason, I avoid all backup software. The extra step of restoring a backup of files stored inside another file is not useful to me. All it really does is it creates a dependency on an added piece of software that only slows me down. The ability to create an archive containing an incredible number of small files can still be useful, though. For that, I'll use WinRAR. FastCopy does everything else (also including the copying of ZIP/RAR archives and/or ISO/other types of image files, like, e.g., Acronis/Macrium images between different storage locations of course).
Hopefully this further explains what I meant when, earlier in the thread, I wrote that I always aim to choose the right tool for the job. These are just my own personal opinions based on my own personal experiences. YMMV