First, the issue with ambient occlusion is a limitation of Eevee.
Eevee uses a technique called screen space ambient occlusion, which means it uses only what is visible on screen and does not actually know the thickness of objects or what is behind them. What you will want to do is play with the occlusion’s “distance” setting and keep it low enough that the effect does not produce obvious artifacts close to thin objects. Sadly, at this time, occlusion in Eevee has to be kept as a low range effect that appears only in narrow spaces, or you have to accept some level of artifacts.
Now, let’s look at the bounce light.
-First, you have to know that the irradiance volume captures bounce light not just from the area light, but also from the actual sky. This is probably causing the bounce light to be too strong, because it’s capturing the light from the window twice. Possible solutions would be to either reduce the intensity of the irradiance volume, or temporarily setting the sky’s strength to 0 while baking the indirect light.
-Second thing, make sure you have “screen space reflections” activated in the render settings and that all materials have their “roughness” parameter well adjusted. In Eevee, this can greatly increase realism by adding subtle reflections on lots of surfaces and making materials look more convincing.
-Third, The irradiance volume could probably use more resolution, especially in the horizontal axes. For a scene like that, I would try something like 12x12x5. If that causes artifacts from probes being too close to objects, you can increase the irradiance volume’s “clipping start” value to solve them. Also, if the increased resolution causes a visible square pattern in the lighting, you can go to the render settings and, under “indirect lighting”, you can play with the “irradiance smoothing”. You will have to re-bake the indirect light to see some of these changes.
Last thing, I see some weirdness in the upper corners of the tables. I think this is probably not caused by the lighting, but by edges on the object being smooth while they should not be. Selecting the object, you can go to the “object data properties” section and, under “normals”, activate auto smooth, which will force sharp edges to be shaded as sharp, depending on their angle.
Hoping some of this will help!