A new version of the ResourceFunction will become available soon. This version as been rewritten and no longer uses the child-taxa property iteratively. This version of TaxonomyTree relies on the TaxonomicSequence and the SpeciesList properties. These properties give results reliably across different installations e.g. cloud, Citrix on a PC.
Version 1.0.0 employed the child-taxa entity property iteratively as a way to traverse the taxonomy tree. Unfortunately, the child-taxa property may not yield any results on some platforms, causing the ResourceFunction to fail.
Comparison of child-taxa resolution performance
My PC, Windows:
Mathematica Online:
Mathematica 13.3. Windows running in a Citrix session:
Of course I tested version 1.0.0 on my PC without any issues, but for other platforms it will not work. I don't think this is how the TaxonomicSpecies entities are supposed to work, so I may report this to Wolfram Support.