I would like my "Quick LINKS" web part links to open in the same tab/window just as the "Quick LAUNCH" navigation bar links open in the same tab/window. I have found that "Pages" in my site linked to quick link web part open in the same tab/window. Lists and libraries open in a new tab.
In that case it seems like you will have to wait for Microsoft to fix it.
On a classic page this could be fixed by injecting a js script, but that is not an option on modern pages :-(