The behavior you are experiencing with the Quick Links web part is expected. According to this article: Think about link target interactions, by default, links to external sites or documents will always open in a new tab. This means that the "Open link in a new tab" checkbox in the Quick Links web part will always open external links in a new tab, regardless of whether the checkbox is checked or not.
If the answer is helpful, please click "Accept Answer" and kindly upvote it. If you have extra questions about this answer, please click "Comment".
Note: Please follow the steps in our documentation to enable e-mail notifications if you want to receive the related email notification for this thread.