I am trying to download a shapefile (polygon) for the 2021 Census Lower layer Super Output Areas (LSOA) for London. I came across this webpage,but whenever I select the shapefile, or geopackage or geojson the geometry is empty (i.e., there are no polygons).

I can easily find LSOA for 2011 but not for 2021. Can someone help me to find the shapefile (or geopackage, or geojson) for the year 2021?

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That page only includes the names and codes for the zones, to be honest I can't think why anyone would want just those. You want the boundaries for the zones which can be found at https://www.data.gov.uk/dataset/d5505463-73e9-4030-9c77-f6596dca1ef7/lower-layer-super-output-areas-december-2021-boundaries-ew-bfe-v9

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