I've found the star cluster that can be seen in the main menu. I didn't manage to find the exact system from which it can be seen though, but maybe together we can do it.
Here's the URL for it: se://v=990&n=Main%20Menu%20Star%20Cluster&b=RSC%200%2D7%2D1384784%2D2225%2D1258%2D0%2D0%2D24%202&p=RSC%200%2D7%2D1384784%2D2225%2D1258%2D0%2D0%2D24&t=+25841CF4603CAE2A53189A17FC&x=-15B1CD4CBD7D5BA09D89829B135A&y=+3E73E3AE23B7988397A6EE833FDB&z=-16556DDBDC1ABD81811EBDD55684&qx=0.3232274&qy=0.5651876&qz=0.5256857&qw=-0.5474866&u=4.275&m=1&s=1&f=0&e=0
And yes this is probably the rarest random discovery in my life since the Earth is 3.82 Gly away from it. I found it by accident - I changed the brightness of the random nebula around the cluster and when I entered the game the next day, the nebula on the main menu was extremely bright. I've tried to pinpoint the location of the planet that can be seen in the menu but to no avail.