refactor: move e2e tests to private infrastructure #6628

Job	Run time
find-dead-code	59s
markdown-link-check	55s
doc-build-test	1m 33s
build-test	42s
pre-commit	41s
Pylint test (3.8)	1m 17s
pyright (3.8)	1m 0s
Unit and integration tests (ubuntu-latest, 3.8)	1m 45s
Pylint test (3.12)	1m 12s
pyright (3.12)	59s
Unit and integration tests (windows-latest, 3.8)	3m 33s
Unit and integration tests (ubuntu-latest, 3.12)	1m 42s
	16m 18s

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