Did you try all the possible ways on MU website to retrieve your booking? Some may be more successful than others, in particular the “Verify my booking” section (even if ticket bought via an OTA). Others may still work if you try some tricks (like adding “ mr” to your first name, trying both 781xxx and 781-xxx).
On a forthcoming trip with MU, I have noticed that the PNR given by the OTA was not my actual MU PNR displayed by their website.
My booking does appear on the AF app though, but I have one leg operated by AF (on MU codeshare). Interestingly, all others legs are shown but STD/STA appear as “00:00”. Needless to say, even if booked in J I can’t select my seat in advance on my AF leg…