Average individual correlations or perform 1 set of correlations

First of all thanks for your time reading this post.

I got some issue with correlation analysis that I am not able to solve at all as for more people I ask, different opinions I get (including opinions read on this forum). I will try to explain my situation:

I go 1200 data from different independent variables (y) and one dependent variable (x). I am calculating the pearson coefficient (r) from each xy pairwise (I don't need multiple analysis). The thing is that I have many different options on doing the analysis as:

1) Data are from different training sessions, in which each sessions are different exercises (i.e. 5 exercises) and from each exercise I have 20 athletes.

2)Resuming, this 1200 data corresponds from about 20 trainings and 80 exercises (more or less).

3) The biggest issue is that de dependent variable is the same number for each player on each exercise (while independent not), and also the same for each session. Of course, it will give a plot as I show on the picture if I use all the players at the same time (with the 1200 data)

My first approach was to make exercises averages (from 20 players per exercise) and also sessions averages (from 20 players per session, the sume of all the exercises on each session). Thus, the dependent variable would be only one different number for each pairwise. But I don't like this approach, as I am assuming to much errors like that.

The second approach, was to make individual correlations throught exercises or trainings for each player independent, so I will have an r value for each player and bivarate correlation. Later, as I need an average r, I made fisher z transformation, ponderate and average and them back transform.

So the doubt is, should I use this last approach of average r values or better should I just use all data together, considering that for many situations, would be too much data that will be the same on the dependent variable for different values on the independent variable?

Thanks for your time!