I don’t know how to solve the problem but here is something I experienced so far. The interlaced 576 picture from PS2 is a bit shaky when captured via Elgato Cam Link. On my Samsung 720p TV the shakyness is unnoticeable. When using Passthrough mode the content captured by Elgato is unwatchable because it just shakes too much. On 2x (bob) I can get rid most of the shakyness. The frames of the picture will still shake but I can get rid of it just cropping them a bit. After this I can still notice a bit of shaking on some texts and lines but isn’t that noticable and I’m OK with the results. I tried all the deinterlace methods in OBS Studio and I found that Blend 2x works best for me. I’m still not using it because it makes some ghosting.
If you set your FPS to 25 (576) or 30 (480) the shakyness will disappear but it’s for you to decide if it’s really worth it. I don’t know if it’s possible to get nice and smooth interlaced image with OSSC.