how do I turn free space into a useable partition? I have read a few answers to this sort of question already, but don't know how to do it. I had some problems with my partitioning, it seems the operating system has been somehow installed on bootcamp, not Macintosh HD.

Obviously Bootcamp is the bottom partition regardless of this and so when I decided I'd just delete the other partition and expand bootcamp I got left with about 70gb free space i can't seem to expand into.

The answer seems to be turning the free space into a new partition and going from there however, the thing I think is meant to be doing this has been saying 'modifying partition map.' for a very long time now and I don't know if it's even doing anything...?
As far as I know you may resize MacOS Extended partitions with Disk Utility but not foreign partitions like ExFAT. One option is to use the restore facility in Disk Utility: restore e.g. on an external disk, erase and recreate a bigger partition, restore from the external disk to the new partition.