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.

[1]: https://datatracker.ietf.org/doc/html/rfc9535

Don't forget the also standardized way of referring to a single value in JSON, "JSON Pointer": datatracker.ietf.org/doc/html/rfc6901

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.

[0] https://goessner.net/articles/JsonPath/

Postgresql supports jsonpath, right?

SQLite might too, though I'm struggling to find anything explicit about the syntax: https://sqlite.org/json1.html#jptr

it might just be a very limited subset?

Looks like "JSON Pointer": datatracker.ietf.org/doc/html/rfc6901

JSON pointer uses very different syntax. Sqlite looks like it uses something that is very similar to, but not quite compatible with, JSONPath.