THINK TANK: SENIOR
For what I've understood at the moment Turkey have just send some advisers and a token mercenary force.
I don't think that Erdogan will seriously commit himself in Lybia, it is just an act of propaganda (mainly for internal consumption imho). He does not have the resorces to invest in a full proxy war against Egypt in Lybia. In order to be successful Turkey would have to project its forces, establishing air bases there, just as the russian did in Syria.
And at the moment I think they lack the resources and the political will to a full scale commitment; let's not forget that Turkey is still entangled in northern Syria, where they would have to remain until a suitable solution is worked out with Damascus and Moscow.
Eygpt and Algeria might get involved now in this matter which will make Erdogan turn the wheel back to Turkey.