"I am looking for new friends."
Translation:Jag söker nya vänner.
I'm not entirely sure but I'm under the impression that söka can be used for figurative expressions (e.g. Söka livets mening) whereas leta efter is more restricted to searching concrete things (e.g. Leta efter nycklar). I guess this would be somewhat analogous to the difference between search vs look for.
Yes, söker tends to be used more in abstract senses and letar in more concrete ones. And it's more common and idiomatic to say söker nya X and letar efter nya X, but the other combinations are also acceptable.
If you do use söker with concrete nouns it tends to come off as a bit stiff, formal or archaic. "I seek my keys"