Are there standards on how a graph database can be queried or interfaced with, that all/most implementations adhere to?
IMHO, SQL took off primarily for those reasons. Widespread use, common standards, and implementations that were easy to approach cemented SQL as the standard used and understood by old and new developers alike.
For true data interoperability, as opposed to the silo data models required for property graph databases, the RDF w3c standard with SPARQL [2] is the industry standard. The new global API made possible with the Solid project [3] by Tim Berners-lee uses RDF
[1] https://blazegraph.com/ [2] https://en.wikipedia.org/wiki/SPARQL and https://www.w3.org/TR/sparql11-query/ [3] https://solidproject.org/
With respect to graph databases, the industry standard is Tinkerpop-Gremlin. Of the top 5 graph databases 4 support it, coincidentally the only one not to support it is Virtuoso. It's not like any other query language I've used, there's quite a bit of learning involved and the docs[1] sometimes lack sufficient detail, there's multiple ways of achieving the same result and unfortunately, some implementations don't provide the full language (eg Cosmos Graph [2] doesn't support the Match step or lambdas). But slowly with handy resources like (Practical Gremlin)[3] and trial and error, you can do some very sophisticated things.
[0]: https://db-engines.com/en/ranking/graph+dbms [1]: https://tinkerpop.apache.org/docs/3.5.1/reference/ [2]: https://docs.microsoft.com/en-us/azure/cosmos-db/gremlin-sup... [3]: http://www.kelvinlawrence.net/book/PracticalGremlin.html
SPARQL and RDF are powering the new decentralized web with a global interoperable api in the form of Solid (by the inventor of the web) - you'll likely be hearing a lot more about this as it rolls out commercially in the coming months
It has a developer mode, where you can run clojuru to query the nodes, I'm starting to use it to create code references between nodes, nothing useeful, but you definitevely can start playing with it
https://db-engines.com/en/ranking/graph+dbms
As for standards, absolutely. Gremlin and TinkerPop are both common ways to interface with Graph Databases that work across many different vendors.
That said, IMHO graph databases are pretty niche. SQL took off because the ability to normalize data when you store it and then relate it as needed when you query while still getting great performance for large-ish data (thanks to indices and query optimizers) is really powerful.