Recently when I got aware and started my LD, I got a confusion as to am I really lucid dreaming or am I just imagining things lying in my bed. And to my disappointment, I opened my eyes without any struggle. But I am sure at the moment I got aware I was dreaming.
Nice experience!
For me, the dreaming world is as real as physical reality, what do you think about that? Neither is more “important” - they both feel real!
Apparently people will most naturally become lucid when they are about to wake up, so the lucid dream will be very short. What you describe sounds like the experience of dreaming when you are almost fully awake, just on the border between the two states. A better experience is to be fully asleep but just awake and aware enough to think rationally and recognise any oddities, or recognise that the world has a different quality about it that is not the same as waking reality. Try and remember what it was like to be in this sleeping/awake state and when you are able to think clearly enough, recognise it in a full dream.