This is interesting Q-A to read: How is the unwanted cold welding prevented in space?
Interesting to read paper they refer:
Assessment of Cold Welding between Separable Contact Surfaces due to Impact and Fretting under Vacuum
Cold welding test method
The contact is closed for 10 s and then and opened for another
10 s. At impact, the base pressure of the vacuum is less than 5 × 10–8 mbar, i.e.
the surfaces are not recovered during opening. During a fretting test, a base
pressure of 55 × 10–7 mbar is sufficient, since the change from oxidative to
adhesive wear occurs in the range 0.1–10–3 mbar.
In appendix they recommend pressure for testing:
But it have to be understood, that process depends from set of factors, including type of interaction between parts, and not induced by vacuum, but induced by lack of gas which will form or restore adhesive and chemical layers over surface of metal fast enough, to prevent cold welding to happen.
This video as example is also cold welding, there protective layers are destroyed faster then they can form with that metal-metal sealing.
So answering the question, starting from medium vacuum(1 – 10−3 mbar) we have to consider and expect it to happen, but it highly depend on parts(their material) and their working conditions.