Thank for posting @BrennanSmith1
Here is an alternative, not a perfect alternative but another option using the CIM.
This will not update while the APRX is open, if you run in an open CURRENT project you will need to close and reopen. If you run in a standalone script, one you reopen the APRX the layers are sorted.
import arcpy
## access the aPRX
aprx_path = "path/to/your.aprx"
aprx = arcpy.mp.ArcGISProject(aprx_path)
## access the Map
m = aprx.listMaps("Map")[0]
## get the CIM definition
m_cim = m.getDefinition("V3")
## current order
##for tbl in m_cim.standaloneTables:
## print(tbl)
## sort
m_cim.standaloneTables = sorted(m_cim.standaloneTables)
## set new definition
m.setDefinition(m_cim)
## open aprx and see the change.
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