First off, I should introduce myself - I've taken over from Lawrence Kelley as the maintainer/developer of Phyre2; please bear with me while I find my feet and am not able to give definitive answers quite so readily (Lawrence worked on Phyre for ~20 years and I have only been "in charge" (whatever that means) since the end of November 2020; our overlap time was affected by current events...).
To answer your question in a general way; without searching the PDB for human somatic GAPDH, I don't know which PDB IDs relate to these proteins - so if you could give the PDBs of expected matching structures, it saves me a lot of work.
Having said that, it wouldn't surprise me if there are none of the structures you might expect included in our fold library, because in order to save time when finding homologous models, we don't store the entire PDB in our fold library - just a large set of proteins with the known folds (which was originally based on SCOP70 but has expanded over the years ). It's interesting (and predicted by people like Cyrus Chothia and Sarah Teichmann many years ago) that most folds seem to have been discovered already (there have been very few new folds being added to the PDB over the last 10 years, for example).
It's likely that the 3H9E structure is similar to the human somatic GAPDH structures you expected.
Your "initial thought" was incorrect - as you found out, the fold library does contain information about individual chains in multimeric complexes. So, if you see a hit with a name like "c3g73A_" the "c" stands for "chain", the "3g73" is the PDB ID, and the "A" means the "A" chain in that entry (which actually has two polypeptide chains and a bit of DNA...).
I hope this helps