Basically, it is not a link the Instagram module expects. Expected links must be the direct links to the image. Such as, https://www.example.com/image.jpg (.png, .mp4, etc.)
Is there anyone who has experienced the same issue and/or has a solution for this?
Thanks for your answer. Definitely, I will consider that.
The same scenario has been working properly since that day. How do they detect that the link is used in the Instagram API and block it? If that is the issue, I did not see anyone who experienced the same problem.