What do you mean by Rust-based? The framework should be written in Rust or are you only interested in Rust bindings so that you can write your code in Rust? I'd recommend looking at Burn, Candle and the Rust Torch bindings and see what you like / performs best.
Burn, candle and torch all support the conversion of ONNX models to their native representations. Burn and candle are written in Rust. Torch—arguably the most widely used deep learning framework in the world—is a C++ library with a Rust wrapper.
I've looked at the docs a bit more and looks like Candle can only run inference on ONNX models. Burn has a converter that converts ONNX models to their native tensor format. I've not read anywhere that either only supports a subset of the ONNX format.