Frankly I think our conception is way too limited.
For instance, I would describe it as self-aware: it's at least aware of its own state in the same way that your car is aware of it's mileage and engine condition. They're not sapient, but I do think they demonstrate self awareness in some narrow sense.
I think rather than imagine these instances as "inanimate" we should place their level of comprehension along the same spectrum that includes a sea sponge, a nematode, a trout, a grasshopper, etc.
I don't know where the LLMs fall, but I find it hard to argue that they have less self awareness than a hamster. And that should freak us all out.