Two chefs in a kitchen wouldn't shorten the development time. Besides, the power outputs of the engines are not similar.In my ignorance: setting politics aside, which could preclude co-developments
(estimated)
1 How long for Turkiye to develop TF35000 alone?
2 How long for ROK to develop an engine for Kf-21 alone?
Could time be saved through the 2 countries sharing technology? I guess that there must be areas in which one country is ahead and other areas where the other country is ahead.
Current KF-21 is a bit small for it to have an IWB. Maybe a larger version in the future could require TF35K level of thrust and the Koreans could become interested in the Turkish made engine.
But that's way into the future. First we need to see some progress regarding TF35K.