Got the ESP-IDE working and tested raw performance with the iperf example from the ESP32S3 to my Desktop. Got roughly 45Mbit/s in both directions.
Meaning the hardware itself is capable.
Now I will write the ESP-IDF version of my snapshot camera program to see if using their examples changes the HTTP-Post throughput.
I also tested my server implementation. This is definitively not the bottleneck. On my small homelab it has no problem with concurrent 30 files/sec