Both of your options presume there is a difference between a conscious mind, and an unconscious mind. These options intrinsically reject a variety of mind models, such as reductive eliminativism, neural identity theory, most idealisms, or delusionism, as they do not support your assumptions.
The conscious/unconscious boundary assumption requires some version of emergence, or ontological dualism. Emergent physicalism is the most common family of physicalist views, and both Popperian emergent dualism, and spiritual dualism both would support this unconscious/conscious boundary assumption for qualia, so there are a spectrum of mind theories that can be referenced here.
There are several research efforts on consciousness that seem like they could shed light on your question. The most useful I have found is David Eagleman's neo-dualist model of our unconsciousness using qualia "props" to create the illusion in our conscious mind of a fully fleshed out stage of the world which is then used as our world model in our "mind's eye". This is spelled out in his book Incognito: https://www.goodreads.com/book/show/9827912-incognito. Some of what is passed to our consciousness are detailed sensory quales, others are basically logic categories, such as "there is something over there". One key point Eagleman points out is that we have far fewer actual quales of perception than we THINK we do, because of so many sleight of hand logic frames that are passed rather than actual quales. Note, it is ME saying Eagleman's model is basically dualist, Eagleman considers himself to be a physicalist.
Additional test data set I find of great interest is the decision logic experiments of Daniel Kahneman, documented in Thinking Fast and Slow. Kahneman postulates that we have two mental systems, system 1 which is basically a neural net processor, and system 2 which is logical/algorithmic. Kahneman does not distinguish between consciousness and unconsciousness, but almost all of our formal reasoning is conscious, and our neural net processing is mostly unconscious, so his system 1 can be treated as an unconscious neural net brain, which feeds selected conclusions and data to a conscious reasoning system for a double-check on what the neural net processing recommends. Note, Daniel Dennett also thinks we have two systems in our heads, and refers to most of our mental processing being neural net processing, but considers that we run a "virtual von-Neuman machine" on our neural net hardware. While Dennett denies we are conscious, his concession to a two-system process is a significant admission from one of the giants of the field.
Two systems requires the interface you reference, as data is passed from system 1 to the conscious system 2, and whether that data is qualia, or whether system 2 generates qualia from that data, is a significant question.
Studying how the two systems interact can address this point. IF system 2 questions system 1, and wants more information about a problem -- such as "show me more details about the 'thing over there'" -- this appears to be system 2 doing thinking on its own, NOT just being fed qualia. And the units of experience behind "show me more details" are themselves qualia, even if system 2 is deluded (per Eagleman) that there are even two systems, or that it is asking a question of another system rather than of itself. So -- qualia can be states of the conscious system.
However, the blindsight experiments done by Nicholas Humphries are also highly informative. The unconscious mind can communicate information to the conscious mind without qualia in blindsight. But the degree of confidence system 2 has in this qualia-free data is greatly decreased. That confidence is ITSELF a qualia, which is self generated, once more showing qualia to be a state of system 2. BUT -- the difference in confidence between data that provides sight qualia, and data that does not, strongly suggests that system 1 is generally providing sight qualia to system 2. Therefore the answer to your question is very plausibly "both".
Therefore a tentative conclusion: System 1 provides qualia in much of its communication with system 2, and system 2 also uses qualia it generates for itself in thinking.