That definitely helped:
On my iPhone under Settings>Music>>Sync Library had not been enabled.
Now checked as one:
Voila: All PayLists button appeared on iMac and clickable.
But only 6 items displayed,
The original Playlist cerated (like forever (residing on MacBook Pro) is very, very lengthy
-- at least 100, more likely > 200 or more .
And now there is an item showing in Music on MBP with the active rotating circle --> Updating Cloud Music Library
But still only 6 named lists showing in the All Playlists on my new iMac . . . .
WRONG! Now truly ALL Playlists are present on new iMac!!!!
and Music on MBP is still Updating Cloud Library