OSM manuall tile server build performance tuning

Dear folks,
I am starting a new thread regarding the openstreetmap-carto / mod_tile configuration. Specs of the used environment:

Debian 12
8 cores
32GB RAM
500GB HDD (spinning disks)

Reference:
Switch2OSM Debian 12 manual build

I have started setting up a full tile server. Anyway it is up and running, but I am still struggeling with performance. I have already switched hardware specs up and down and checked monitoring for faults. All in all I went to the systems journal and will expect several log lines like

renderd[1253807]: Failed to read cmd on fd 20

or

renderd[1565694]: Sending NotDone response(4)

I will use the provided sample html file to browse my tiles. I experience greyed parts in my world map. (just rendered germany for testing) How can I achieve that the rendered service will not throw Sending NotDone response / no grey fields during scrolling through my map?

thanks in advance to all repliers!

regards