Carnap is unlikely to be identified as an existentialist philosopher. In being a Logical Positivist, he clearly belongs to the “analytic philosophy camp”, even if most contemporary “analytic philosophers” do not show a great deal of respect for Carnap and certainly wouldn’t characterize themselves as logical positivists.
Existentialism, on the other hand, is clearly “continental philosophy”. So Carnap cannot be an Existentialist. But this is of course a classical case of forgetting what made philosophy in the first half of the past century an exciting activity, which it since has ceased to be. For back in the day, when you identified as an “analytic” philosopher, you were primarily talking to those philosophers you suspected not to be on your team. Today, when you say you are an analytic philosopher, what you mean is: let’s not even bother to read those other dudes.
So, non-rhetorically speaking: is Carnap an existentialist philosopher? Well, there are important existentialist themes in Carnap’s philosophy. Like the idea of radical freedom, which finds its expression in Carnap in the idea of Tolerance when it comes to adopting ways of speaking. Carnap understood that the search (in particular) for THE TRUE LOGIC was a hopeless endeavor, not because we are too dumb, but because there is no such thing as THE TRUE LOGIC. In fact, we are free to adopt whichever logic serves our purposes, provided we are clear about it.
But the point actually goes beyond that. Carnap strongly distinguished between theoretical questions and practical decisions. While theoretical knowledge can help you in your decision making process, no amount of theoretical knowledge can do the job of making a practical decision. That decision is still and forever up to you! Now, if that doesn’t sound existentialist…