I'm not an expert in Petri nets, but they are definitely used for modeling in various fields. Krohn-Rhodes theory also claims some successes if you read that article.

As for the stuff I'm actively working on: even if it is successful, and uniquely suited to solve some particular problem, I'd imagine it would take at least a few years to be actively applied in the right places -- and it might end up being me helping to apply it!

If you look back at for example graph theory, it was explored on the pure mathematics and computer science side for many decades before it spawned e.g. network science and got applied in sociology, economics, etc.

So, yeah, don't hold your breath! If you'd prefer not to read any blog posts heralding XYZ as the next big thing before XYZ has already led to a concrete breakthrough, I think that's a totally fair. I myself am quite happy to work quietly on things until there is a satisfying and complete application, but Stephen isn't like that. Both stances have pros and cons.