The following passage is from Grammarly 1:
The present perfect tense is one of the common verb tenses in English, used to show an action that happened in the past that is directly related to the present, such as actions that are still continuing or that indicate a change over time.
So I have read a lot of books since I was a child doesn't mean that I read the books and I now I don't read books anymore.
The following text is from Cambridge Dictionary 2:
Present perfect continuous: uses
Recent past activities
We use the present perfect continuous to talk about a finished activity in the recent past. Using the present perfect continuous focuses on the activity.
We don’t give a specific time. Even though the activity is finished, we can see the result in the present:
I’ve just been cleaning the car. (The car is wet and clean.)**
It’s been snowing. (The ground is covered in snow.)**
What have you been buying?
One continuing event
We use the present perfect continuous for a single activity that began at a point in the past and is still continuing:
I’ve been reading your book – it’s great. (I’m still reading it.)
He’s been living in the village since 1995. (He is still living in the village.)
She has been writing her autobiography since 1987.
Repeated continuing events
We use the present perfect continuous to talk about repeated activities which started at a particular time in the past and are still continuing up until now:
I’ve been going to Spain on holiday every year since 1987.
I haven’t been eating much lunch lately. I’ve been going to the gym at lunchtimes.
She’s been playing tennis on and off for three years.
How long …?
We often use the present perfect continuous to ask and answer questions about the duration of an activity. We use the question How long … + present perfect continuous:
A: How long have you been waiting for me?
B: About ten minutes. Not too long. (I’ve been waiting for about ten minutes.)
So both your sentences I have read a lot of books since I was a child and I've been reading a lot of books since I was a child are correct.