Hello Fennx. I found something that can help you with the issue.
I will provide you with the solution that someone on the forum discovered for this issue.
“The install got stuck at 82%. This is the point where the download is done and the unpacked files are sitting in .egstore. I was waiting for two hours but nothing happened. It only continued for me after I restarted the Epic Launcher with admin rights. Right after the restart the normal Engine folder of the installation appeared and got filled.”
Let us know if it worked for you; I await your message.