Most of the time, I remember many of the dreams I hadve.

I added most of the time, since it just sounds more natural and you put “many of the dreams” (which implies that you don’t remember your dreams all the time)

I used to write down interesting dreams in my notebook, but not now, because many recent dreams I can tell which areI don’t anymore, because many dreams recently/lately have been reflections of reality, which isare boring to me. and not worth writing down/recording.

You don’t need to put “now” here, since you already have “recent dreams”

But even though I don'’t easily forgetwrite them down, I still remember some specific scenes and events in those dreams and I recognize the existence of—some which I think are precognitive dreams.

“Don’t easily forget” is kind of wordy and it would be more simple and straightforward to just say “remember”
To clarify the “but” here, I put an explanation so readers can understand it better