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'' Because Mongo's APIs are unique (not a standard, no third-party implementations), would this mean that your software is derived from MongoDB? Yes it would, simply because without MongoDB it couldn't function. ''

According to the recent EU ruling your program is derived from MongoDB's API. But to prevent 'monopolization of ideas', MongoDB APIs are not under copyright so your software is not a derived work. In addition the ruling voids license clauses with conditions on how you run the software past normal use, so clauses like 'except you can't clone the API' or 'can only link with approved software' or 'have to publish the signing key' are unenforceable.

Since it's not a derived work and GPL linking restrictions are not enforceable, you simply accept the GPL and distribute the .so and source for that code along with your closed-source program and use it. You still have to publish your changes to the GPL code itself, like LGPL, but that's all.

This is the flip side of the API-copyrightability coin.