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The jitter is because it's usually rendered at 50% resolution - you can render it at full framebuffer size and it doesn't jitter but it's kind of hard to justify.

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That might be part of it, but the effect I’m describing includes the shading changing shape. So for example if a bust on a pillar is sitting in a corner, as the camera pans around the bust, AO behind the bust shifts to “wrap” around the edges of the bust which looks strange because no shadow in the real world acts like that.

This is largely because early screen-space AO techniques weren't able to accurately estimate whether the pillar is freestanding (and shouldn't darken the wall) or if it is against the wall (and should darken the wall.)

Modern real-time ambient occlusion techniques can estimate the depth far more accurately and produce correspondingly more believable results, at the cost of performance.

https://www.researchgate.net/figure/Visual-comparison-of-dif...

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