I should study more in depth and open some ticket but I writing this problem down here, otherwise I’ll forget (I already forgot this once or twice recently, now another time I come across it, I don’t want to have to remember it myself):
SACEM used to have a short integer ID for works.
Now they use something that looks like our Disc ID and work permalinks no longer work, we have to use work search URL instead (cf. second edit, lower).
I must verify that they are actually work ID and not search session ID or seomthing bogus like that.