It is sounding like a bug in UE5.1 but more information would be helpful for Epic and others to view.
If it works OK in 5.1 without any LODs (in other words, just LOD0) it shows your skeletal mesh is working ok and it must be the LODs.
If it works ok from a Migrated 4.27 project, it shows it’s the creation/importing of the LODs that is the problem.
Just an offchance, they do seem ok, but I’m assuming all the ScreenSizes are correct for the LODs? LOD0 has a SizeSize of 1.0 and the others are smaller - say less that 0.5?