Bake HDRI lighting within light probes

Before I start, I am using Blender 3.0 with Eevee. I am familiar with creating Irradiance Volumes and Reflection Cubemaps to bake light into my scenes via Emission materials. What I am currently trying to do is apply this same process using HDRI images from Polyhaven. When you bake lighting, it generally stays within your scene’s probes. However, when I tried this with an HDRI, it bakes the lighting into both the probes AND outside of it. The area I want the lighting looks good, but the area outside (where there shouldn’t be any light), is actually double the strength, and even disconnecting the HDRI from the World Output doesn’t get rid of it after the bake is complete. Maybe this is a noob thing I’m missing, because I’m not claiming to be an expert by any stretch of the imagination. Can anybody help?

One thing irradiance probes do is shadow the light from the background. If your volume is in the middle of some objects and the main light source is the backround, the probe is mostly going to have a darkening effect as the HDRI gets shadowed by those objects. However, the areas outside the probe won’t get this shadowing effect.

Are you saying that the HDRI’s effect actually gets stronger outside the probe compared to before it was baked?

What happens if you disable the HDRI from the Camera Ray visibility in the world settings before you bake?