Watched the video, and I thought it was really cool seeing the modeling of different young solar-systems. The orbital resonances they were talking about were for smaller objects that form debris fields in resonance with a giant planet. Since they only looked at models for the inner planets, the closest example to the bit in the video with our current solar-system would be Jupiter's Hildas. For that specific part of the video, they only showed one inner most giant planet. For more than one, Resonances like that are unlikely to form between giant planets, like in our solar system where most of the resonance objects fall inside Jupiter or outside Neptune.
The mathematics gets too complicated for me to know for sure, but as I understand it, planets in resonance is neither stable nor unstable, unless the aphelion of one planet is in resonance with the perihelion of another, in which case the planets could drawn together I would think. That's my amateur answer to your question. I wouldn't think orbital resonance affects stability.
When one planet is dominant and the other quite small, then resonances appear largely stable (Neptune/Pluto for example), provided they never get close to each other, which Neptune-Pluto don't.
Jupiter and Saturn were thought to have entered orbital resonance at one point in the early solar-system and that, from what I've read, affected other objects in the solar system but didn't affect their relation to each other much. I think the only way to get any kind of answer is to run long term simulations on various model. In short, planets can be stable both in resonance with each other, and not in resonance and planets can be unstable, again, either in resonance or not in resonance, though if they have unstable orbits, they won't stay in resonance for long.
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