Alright, here is a final update after months.
Due to personal circumstances it took a while to get to the experts I meant. FYI, these experts worked in a shop called ReplaceDirect. This shop repairs and sells a lot of stuff for smartphones and laptops.
I personally went there for the 2nd time in years and noticed that the experts don't work there anymore. Instead there was a foreign tech guy (from his accent) who I think didn't quite understand me, he kept blaming the GPU for the cause while I tried to explain that the GPU was installed months after the issue started. After a (nice?) conversation they said there wasn't anything they could do, they only repair smartphones and laptops because they have the equipment for that. He mentioned that he could run software tests to diagnose the issue, which I already had done tons of times, but nothing more.
After I finally came back home, I decided to first prepare a RMA for the motherboard instead, from what I read about similar issues the motherboard is more often the cause than the CPU. I went to the Gigabyte support page for my motherboard and noticed that after 8 months 3 BIOS updates were released. 2 BIOS updates are released to provide support for the 7th generation of CPUs and 1 of them for improving VGA compatibility. I thought that installing the newest update may help something. So, I downloaded the BIOS, booted into the BIOS and made a BIOS backup first, then I installed the update and booted into Windows.
The first impression I had was that Windows somehow became extremely laggy. In The Witcher 3: Wild Hunt I would usually get around 50-60 fp/s, this time it was between 20 and 40. Even while doing nothing the system was extremely laggy. I booted into safe mode to find out if the lagging also existed there, fortunately this wasn't the case.
I decided that my next move was to clean install Windows, after backing up everything I didn't want to loose and so I did.
A few hours after a clean Windows I was mainly done with installing all stuff (programs, drivers, customization where I wanted, games).
After reinstalling Windows and everything, I noticed 2 issues I didn't like.
1. The EFI partition was on the HDD, while I installed Windows on the SSD, partitioning was kind of a chaos
2. The HDD partitions appeared to be a dynamic disk.
To solve the dynamic disk issue, I downloaded the recovery tool from @
Kyhi and used Minitool Partition Wizard to easily convert the dynamic partitions to basic.
To get the EFI partition on the correct location, I deleted the partition from the HDD and disconnected it. Then I wiped the SSD and again clean installed Windows on it.
The EFI partition was most likely installed on the HDD, because the HDD was seen as Disk 0 by Windows, so I switched the sata ports between the SSD and the HDD so the SSD is now seen as Disk 0.
I wiped the SSD on the 17th for the last time and have had no single issue since. I have finally been able to do all the things for which I had built the system.
The final blame looks to be BIOS version F3, I have no idea why but I guess it was some kind of a bug with it.