It wasn’t specific in the 7/29 TWAB. It just says Console (with Stadia).
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Based on the brief "beta" they did back at the end of May, I would say yes. I took part in that while playing on my Xbox One as well as PC and had no issue. Besides, if they weren't going to support the older gen consoles, they would have indicated it the same TWaB. I know that Bungie doesn't have the best track record on their communications, but holding back on information such as not supporting old gen would not have gone over well with the community. This would be like them holding back on announcing they would no longer be supporting the PS3 / 360 consoles when RoI was released.