For reference, I was using 'https://pokedens.github.io/' which is clearly incorrect.
However, using Kaphotic's pastebin data, it appears Shield can have Hidden Ability Flygon, but not Sword. Likewise, it is indeed not possible for Shedinja to have its hidden ability in this games, confirming that. Are you aware of any other pokemon which can have their hidden ability flag enabled in Sword/Shield which has no effect? Is there a full, correct data set out there, after all a lot of data on said pastebin marks Hiddens I've never found.
Edit: Looking at the src of the plugin you mentioned, I'm seeing what I believe to be HA capabilities (HA marked as 4) in the tables, which implies available, including Shedinja. Is it potentially a seed related issue?