[Feature Request] Support building Python-API for multiple ExecutionProviders

[ORippler]

Describe the feature request

Currently, apparently there is no "official" support for building onnxruntime with multiple ExecutionProviders, see also #18790.

The issue I linked to suggests building onnxruntime from scratch as a resolution, and I did exactly that.
However, there were several places in the (python) code where it's hard-coded/assumed that there is only one ExecutionProvider available. Two most prominent places that come to mind (and should be considered bugs if onnxruntime says it supports using mulitple ExecutionProviders in parallel):

1. During building for example, package name and EP-flags such as is_openvino are mutually exclusive while they do not have to be, see e.g. https://github.com/microsoft/onnxruntime/blob/main/setup.py#L62-L88
2. The error detection and fallback logic of InferenceSession are also assuming mutually exclusive ExecutionProviders, see for example here https://github.com/microsoft/onnxruntime/blob/main/onnxruntime/python/onnxruntime_inference_collection.py#L437-L460. This lead to the inability of falling back from OpenVINOExeuctionProvider to CPUExecutionProvider when the available provider list is ["TensorrtExecutionProvider", "CUDAExecutionProvider", "OpenVINOExecutionProvider", "CPUExecutionProvider"], which is the case when compiling with trt, cuda & openvino.

Both of the above should be considered bugs that need to be solved if onnxruntime decides to actually support multiple ExecutionProviders officially

Describe scenario use case

Deployment inside docker where one wants to leverage multiple EPs/different hardware sets, see also #18790