There is a standard in RFC 9535 (JSONPath)[1]. But as far as I can tell, it isn't very widely used, and it has more limited functionality than some of the alternatives.
the issue with JSONPath is that it took 17 years for it to become a properly fleshed-out standard. The original idea came from a 2007 blog post [0], which was then extended and implemented subtly differently dozens of times, with the result that almost every JSON Path implementation out there is incompatible with the others.
[1]: https://datatracker.ietf.org/doc/html/rfc9535