You are in the right path, we need just need to use authenticator on the new contact list and product selected and get supervisor's email address

Thanks rondev for the response, however I still don't fully understand. I will break my question down a little further for clarification. Firstly, what do I have as my choices for my multiple choice question? Will these have to match the project names in my second contact list, or is there a way to link these so that the choices are piped text from the contact list? Below is an example of the question.

Secondly, is this how I should have my second contact list set up?
Thirdly, how does the setup look like in the survey flow? Below is a screenshot of what I have setup at the moment. The supervisor contact list is labelled as Test.
Thanks in advance.

Will these have to match the project names in my second contact list - Yes, it should match with the contact list.
Also, as we can only authenticate based on email and ExternalDataReference column, we need to put projects name under ExternalDataReference column in contact list.
Regarding setup - The value of project embedded data is I guess set wrong, please do the correct piping. In the authentication field, their will be only external data reference. Check the 'prefill' checkbox and enter 'Project' in the text entry box that will appear after checking prefill checkbox.

Also put supervisor's email in some other column(embedded data eg: Semail) and add same name embedded data (Semail) under authenticator in survey flow.

Now that I have set up an authenticator with the second contact list, when I send the survey out to my first contact list (the students), I get this screen asking for the respondent to log in.

Did you use the prefill option?

Yes this is my survey flow. Do I need to have the embedded data field before the authenticator branch? Am i linking the "Project" embedded data to my multiple choice question or my ExternalDataReference?

Am i linking the "Project" embedded data to my multiple choice question or my ExternalDataReference? - Multiple choice question answer.
Also the embedded data and authenticator will come after project selection question. and the flow will be as below:

Thanks so much rondev, I have managed to get it working. I now have a survey that allows students to select a project, once the survey is completed the supervisor of the selected project is emailed to notify them that the student has selected their project.
I have also set up in the email trigger a link that allows the supervisor to view the students selection and then continue to the next page which asks the supervisor if they accept the students registration or reject. If they accept, the student is emailed to confirm the registration and the process is completed.
I would like to add another element to the survey but I'm not sure if it is going to be possible or if is going to course to many issues when sorting through the response data.
If the supervisor rejects the registration I would like it to email the student with some kind of link so that they could either take the survey again or retake their original response and select a different project. The issue I am having is how the survey identifies if it is the student retaking the survey or whether it is a supervisor. The supervisors URL contains "DEL" or "Q_R" which is how I differentiate between the two during the students first response but when it comes to them retaking the survey, it also contains it. Any feedback or help is appreciated.
My survey flow looks like this: