After receiving sensible advice (@matrix) to check my internet connection speeds, here's what I got. My connection speeds are... well, it depends!
#1. Tethering with usb cable:
https://librespeed.org/results/?id=11lu855
Ping: 36.6 ms Jitter: 4.56 ms Down: 3.17 Mbps Up: 68.0 Mbps
#2. Tethering with WiFi
https://librespeed.org/results/?id=113rv7d
Ping: 38.4 ms Jitter: 26.7 ms Down: 43.6 Mbps Up: 51.8 Mbps
#3. Internet connection with "dongle-type" 4G USB Modem
https://librespeed.org/results/?id=12kola1
Ping: 29.9 ms Jitter: 3.12 ms Down: 104 Mbps Up: 47.2 Mbps
According to these results Solus Software Center isn't the culprit here!
Although this solved one problem (slow update), I got now a new one!
For me it would be perhaps the most convienient and sensible way to use option #1 if only the speed wouldn't drop so dramatically.
I really would like to find out what's going on there. Any ideas?