Not to disagree with any other advice for this repair... Just putting forward my own approach and with a reasonable amount of expertee..
I do maintain for that "rather unique" repair Super glue will work... If the veneer separations were more accessible I would use a conventional wood glue (as I usually do)..
Those open edged separations will allow the thin super glue to run deep into the separations/cracks... IMO not enough substance left in that fragmented ply... and it would hardened/ doped by the process.
I have often used Super Glue to repair/fill minor separation of bearing edges... the main downside being that it will darken the grain..
Cheers
John