If Turkey and Egypt were such influential or powerful in Libya, Libya would not have been a mess for 10 + years by now. No outsiders can fix the problems of a foreign country. If that was the case, Yemen would have been one of the most prosperous nations on the planet since it borders one of the most wealthy and stable nations on the planet (KSA) and the Switzerland of the ME (Oman).
It is the same story in all unstable/weak Arab states whether Syria, Libya, Yemen or partially Iraq. If you have a strong national cohesion and a strong state (which includes military, civil society, state institutions, national interests before tribal, ethnic, religious etc) outside meddling like seen in all of those countries (which the exception of actual invasions as the case with the US invasions of Iraq), would not have succeeded. It would have been repelled successfully.
Also the average Arab and average Turk do not have any problems with each other. Don't forget that Arabs are one of the largest native ethnic groups in Turkey and nowadays only Turks and Kurds are larger groups in Turkey.
Even at the height of GCC-Turkey "conflict" Arab tourists continuing visiting Turkey and buying Turkish land, property, making investments etc.
Most likely either KSA/GCC states or Russia just saved Turkey's economy partially.
Ankara is looking to receive an initial $10bn deposit in Turkish bonds and accounts following rapprochement between Erdogan and Mohammed bin Salman
www.middleeasteye.net