Yes, so there's a window, it's supposed to reflect a character (and any other things that move in the vicinity).
The window does show a reflection, but the reflection is static. It shows the character in the T-pose or whatever pose it had when loading up the scene. I think you were right and the issue is with the shader of the window and not the settings for the Reflection Probe. Obviously other items (like Cur's mirrors or Conq's glass planes that I'm looking at now) have realtime reflections.
With the Graphics plugin (which is decently powerful imo) we can set up reflection probes
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So we can get pretty lifelike lighting and reflections. It just takes a lot of trial and error to get it to look good.