I'm not very familiar with latexdiff, but it seems at least some of the annotation of differences is done using \DIFadd{...} and \DIFdel{...} to indicate added and deleted text.
If that is the case, TeXcount can count these by adding macro handling rules for these two macros. One method is to include the following instructions for TeXcount in the document:
%TC:newcounter add Added
%TC:newcounter del Deleted
%TC:macro \DIFadd [add]
%TC:macro \DIFdel [del]
What these TeX comments do is provide instructions to TeXcount (%TC:...) which define two new counters, and then define macro handling rules for \DIFadd and \DIFdel which each take one argument to be counted using these new counters.
These lines need to be included in the difference file, but if you add them to the tex file they should pass through the diffing. An option is to put them in a separate file which you include, but then you need to run TeXcount with the -merge option to insert the included file.
TeXcount has an -opt option which could have been used, but unfortunately this does not work as intended: eg it does not handle the newcounter instruction.
NB: Beware that words counted as added or deleted in this manner are not included in the other word counters. It is possible to add counters together in the summary output when using templates, eg to get total number of words before and after.
perlscript that just concatenates all the arguments of \DIFadd and \DIFdel (separately if desired) - but the result would generally not be valid latex, so I am not sure how well texcount would work on such a concatenated list. – frederik Sep 08 '21 at 10:04