I have the same problem , refresh LR S is still at 2021.31.101 with last update shown as Sept9 ( which is when the care was made I assume), took delivery in Toronto Sept 25. no problem with regular wifi, set to advanced. (my 3rd S so know how the downloads work)
had service check several times and said controlled by factory so they cannot do anything, that no downloads available for my vin and not yet put on to the download system yet. glad to see others with same problem as thought they just forgot about my car. another Toronto same car built 330 cars earlier already has all updates. the only thing with mine was that after it went from dealer to my garage, I actually only started driving it Oct 19 and previous to that it did not have wifi and not likely connected to cellular (as was in my garage).