[DO NOT REVIEW][DO NOT MERGE] Removal ONNX dependency #11511

Job	Run time
Smart_CI	26s
Build / Build	46m 29s
JS API	2m 24s
Samples	9m 34s
Python unit tests	12m 42s
CPU functional tests	38m 18s
OpenVINO Python API Tests (3.9)	4m 32s
OpenVINO Python API Tests (3.10)	5m 3s
OpenVINO Python API Tests (3.11)	4m 35s
OpenVINO Python API Tests (3.12)	4m 34s
OpenVINO tokenizers extension / OpenVINO tokenizers extension	8m 32s
C++ unit tests / C++ unit tests	2m 51s
Pytorch Layer Tests / PyTorch Layer Tests	25m 5s
TensorFlow Layer Tests / TensorFlow Layer Tests	31m 59s
ci/gha_overall_status_windows	1s
	3h 17m 5s

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