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Creating an object that is 1) massive enough to observably bend spacetime, and 2) still can be put in a quantum superposition is... not easy.

True... but you might be able to put an object in superposition with another object and separate those a bit within an existing gravity well and observe the implications.

It is. We haven't had the necessary experimental equipment to be able to measure it until recently. You need an extremely precise clock that you can put into a quantum superposition- that's difficult to make.

https://www.google.com/search?q=can+spacetime+geometry+be+in...

Seems like there is a lot of theory discussions around the Internet but not seeing any experimental evidence one way or the other in the first few results.

It's too difficult to actually carry out in practice. You increase the mass, it quickly becomes impossible to distinguish the states.