There reeeeeally won't be any sort of military intervention, and to be honest with you I think the amount of volume with it is mostly politicking on the part of Tinubu and the junta leaders.
Just getting to Niger is an essentially impossible task thanks to its very remote, VERY Sahelan location for every single member of ECOWAS aside from Benin (not exactly a military power) and Nigeria, operating within Niger is an even more impossible task (even Mali, Burkina Faso, and Niger themselves have consistently struggled to operate within the Sahelan and Saharan terrain, let alone countries that either don't have that sort of terrain at all or have only corners of it), and Nigeria's military and political situation is such that it's in no state to go pulling an invasion itself. Tinubu, the recent president, has to deal with a load of political instability because of contestation over his election, and invading Niger would piss off many of the exact people he's seeing contestation from. Not only that, but the Nigerian military is run ragged through years and years of combat with Boko Haram and several other local conflicts in Nigeria, and they really can't just be pulling all their stakes up from their complicated checkpoint systems and deployments in Nigeria to pull an invasion out of their hat.