Dear Andrzej,
I do not see a way to add the prediction distribution to the forest plot using R package meta.
However, there is a function cidprop() in meta with a corresponding plot function. R function cidprop() calculates expected proportions with clinically important benefit or harm which are based on the prediction distribution. The plot function shows the prediction distribution.
The method is describe in the following paper: https://doi.org/10.1186/s12874-025-02733-9
If you want to use cidprop(), I would suggest to use the development version of meta on GitHub (https://github.com/guido-s/meta) which has some changes.
Best wishes,
Guido