A few things I’d check based on what I read about the LG A1 on RTINGS.com: the PS5 uses variable refresh rate on titles that support it, while the XSX does not. HRD is quite dim (relatively) on that TV, so you could try calibrating the HDR and increasing the brightness all around. The TV does not support a refresh rate above 60 Hz, so make sure in all the video settings that they limit the video to 60 Hz. In the review they talk about the LG accepting a 1080p signal at 120 Hz, but dropping every other frame.

And as others have mentioned, the XBOX dashboard may be upscaled from 1080p with poor results (by the console). To me it doesn’t seem like Microsoft puts that much effort into the dashboard.