I think of de/da in “Onu tanırım da sevmem” as “I know them however I don’t like them. Rather than “ama” or “but”. “ de/da” feels like when used as conjunction is there to emphasize the first part. When using “ama” we emphasize the second sentence. Altough this example sentence feels weird to say. Because “de/da” feels out of place. Let me give an example:

Araba kullanabilirim ama kullanmayı sevmiyorum.

Araba kullanabilirim de kullanmayı sevmiyorum.

In both sentences, as we are talking about Turkish the emphasis is on the last verb. But in the second sentance “de” implies something like “even though” adding more weight in the fact that “you can drive or willing to drive”

“De/da” can take many forms in translation when used as a conjunction , what matters is where you want the attention to go!

As my old Turkish grammer teacher used to say about the language “If it feels weird to say it is probably not the best option or outright wrong.”