@aziemzulthe instructor should be able to get you a Join code for the Team. The difference between using a Join Code and a link to the Team is that with the Join code you are automatically added to the Team as a member, where as with a link to the Team the request has to be approved or denied. There is no request generated when a Join code is used. The instructor can generate the Join code and send it to you to join the Team by following these steps (see attached screenshot):
Click the 3 dots beside the Team name>Manage Team
Click on 'Settings' at the top
Click on 'Team code' to expand the section
Click on the 'Generate' button to create a 'Join code' for the Team
Copy and send the 'Join code' for you to use
The only other factor that I noted in your screenshot is that it says the Team is limited to specific groups. If these are Microsoft 365 groups and you are not a member of one of these groups then it could be blocking your request. Also ensure that you are not signed in with other Microsoft accounts in the same browser that could be interfering with authentication.