[CI] [GHA] Align pipelines (#20388)

* add ONNX layer tests

* add parallelism for pytest; add missing stages to win; align execution steps

* add missng shell option

* add missing dep, update marker

* align stages and execution commands; rm parallelization

* enable trigger

* add missing export; rm not-applicable stage from mac and win pipeline

* add missing requirement, rm not-applicable stage

* add missing test parameters

* try to pi onnxruntime version; skip mxnet on mac; correct vars in win

* rm constraint

* skip on win

* use xfail

* remove always(), rm trigger for mac

* return push trigger for mac

.github/workflows/linux.yml

@@ -1,4 +1,4 @@
-name: Tests on Linux (Ubuntu 20.04, Python 3.11)
+name: Linux (Ubuntu 20.04, Python 3.11)
 on:
   schedule:
     # at 00:00 on Wednesday and Saturday
@@ -947,6 +947,16 @@ jobs:
           TEST_DEVICE: CPU
           TEST_PRECISION: FP16
 
+      - name: ONNX Layer Tests
+        run: |
+          python3 -m pip install -r ${LAYER_TESTS_INSTALL_DIR}/requirements.txt
+          # requires 'unit_tests' from 'tools/mo'
+          export PYTHONPATH=${OPENVINO_REPO}/tools/mo/:$PYTHONPATH
+          python3 -m pytest ${LAYER_TESTS_INSTALL_DIR}/onnx_tests -m "not launch_only_if_manually_specified and precommit" --junitxml=${INSTALL_TEST_DIR}/TEST-onnx.xml
+        env:
+          TEST_DEVICE: CPU
+          TEST_PRECISION: FP16
+
       - name: TensorFlow 1 Layer Tests - TF FE
         run: |
           python3 -m pip install -r ${LAYER_TESTS_INSTALL_DIR}/requirements.txt