Handling first 1:1 with manager and team member as an intern?

First, I highly recommend watching my series on how to succeed as a SWE intern at Meta. I'm sure that SAP and Meta are very different companies, but a lot of the same concepts should apply (I recommend checking out the video about working with your intern manager).

One of my team members advised me to have goals, and expectations of the internship ready before going on to 1:1's.

This is a great team member - They are 100% correct! Nobody can read minds, so things are easier for everyone when people's goals are clear and transparently shared.

How can I be realistic and not desperate in explaining my goals and expectations as an intern?

I wouldn't worry too much about the desperate part - Worrying about negative perception is one of the biggest career traps I see earlier-in-career folks fall into as it leads to paralysis and inaction. Your teammate literally opened this door for you, and you can mention this as well with something like, "Hey, my teammate said it would be better for us if I came in with an idea of what I'm looking for, so here it is."

Another communication "trick" to make this better is to use a self-deprecation shield - I do this all the time. After going through your asks, you can say something like, "Let me know if this doesn't make any sense - This is my first job, so I have no clue what I'm doing, haha."

In terms of things to ask for:

1. A dedicated mentor figure that is always willing to answer your questions
2. Thorough and quick code review feedback - You want your initial pull requests to have a sea of comments, delivered within 24 hours. Here's our video on why fast code review is so important.
3. Honest feedback on how to improve every 2-3 weeks - For tactics around this, I recommend this Q&A on getting the most out of mentorship.

Is there any video of the first 1:1 meeting with the manager and team regarding setting goals and expectations out of the internship?

Not for this very specific use-case, but our masterclass about impactful 1:1 meetings should help with that a lot.