I don’t think there are studies showing direct comparisons(that I know of), but it is clear that commercial social media stands to profit from you the more you use the platform and open-source platforms usually stand to lose money from hosting the service. That incentive alone is big enough to demonstrate how more harmful they are.

Replacing real social interactions with virtual ones is harmul regardless of the platform, so at least open source ones don’t profit from addictions and mental health issues(like casinos). Not to mention that commercial options make it hard for you to leave the platform, and not in a “lets make a maze so the user takes longer to get out” but in a “lets stand in the door for days blocking the users exit”.

Also important to note that it is possible to make a commercial social media platform without such aggresive strategies (at cost of their profit), and a open social media platform with aggresive strategies. It just happens that proprietary software can lend its hand to abuse which is not posible in open source. So in practice none of these happen.

So in general I would say that open source social media is completely free of intentional harm and commercial ones will not bother if their platform is harming people as long as it makes profits.