It’s very difficult to use purely reductionist analysis in complex systems like the garden Charles. Compost, after all, is a living entity and the nature of its content evolves with time, even in the NPK doesn’t very much. There are actually proteins produced which are correlated with what gardeners called ‘humus’ and the more that is produced, the better the quality of humus. Worms are producing vermicompost and all that it contains. Bacteria can produce who knows what depending on which bacteria they are. Fungi can do likewise. Tree branches can provide substrate for certain bacteria/fungi which break down lignin, cellulose etc to create unique soil compounds .
I think it would be fairly easy to come up with a suite of biological indicators for compost during the ripening process, in fact researching that for a decade would no doubt add great value to horticulture, but I wonder whether the big compost retailers would actually want that to be done?!