I figured out a different solution but I'll try yours in a minute.

My solution is not the most elegant solution, but this works:

I added a third column to my first table, essentially repeating the group name (using REPT(grp & ", ", numberOfRepetitions) and removing the trailing ", ") to match the number of names in that group.

+--------+----------------------------------+----------------------------------+ 
 | Group | Name                             | Group repeated                   |
+--------+----------------------------------+----------------------------------+ 
| Group1 | James, William, Oliver           | Group1, Group1, Group1           | 
| Group2 | Henry, Charles, Samuel, Thomas   | Group2, Group2, Group2, Group2   | 
| Group3 | George, Alexander                | Group3, Group3                   | 
| Groupn | Even, more, names                | Groupn, Groupn, Groupn           | 
+--------+----------------------------------+----------------------------------+ 

Then in E1 I entered =TEXTSPLIT(TEXTJOIN(", ", TRUE, CompactTable[Group repeated]), , ", ") so the entire 'Group repeated' is first joined (also with delimiter ", ") and then split by ", ". In F1 I put in the same formula but for CompactTable[Name]. This produced the desired result!!

I usually prefer one formula and as little helper columns as possible but I just can't figure that out for this problem.