You are doing an entry level job, because university has prepared you with the theoretical background to understand the problems you need to solve, but a large part of being a good programmer is experience, which you still lack, and can collect only over time.
If you are at a good company, they will give you a good mixture of tedious "tick-all-the-boxes" and slightly more interesting "learn-all-about-X-and-apply-it" work. Both of these are important learning experiences for you at this stage:
At university, software was finished when it would fulfill the task it was designed to, given proper input. Now your software will have non-expert users, so your program will be given invalid and contradictory input, and needs to recover adequately. Turning a proof-of-concept program into a finished product is an aspect of the job that isn't usually taught in depth at universities, because it is a moving target, and the feedback loop back into the university would be too slow.
At the same time, you are still a bit on probation. Your code output will be monitored and reviewed by more senior programmers, and ideally there will be a fast feedback loop that can tell you within a few minutes to hours whether your code meets acceptance criteria and how to still improve it even if it does. If there is no such mechanism, push for one.
It is in essence an extension of your studies, except that you get paid, and you add the time to your CV under "work experience" rather than "education". In this field, there is no such thing as being finished with learning, and the definition of "full stack" will look completely different in five years.
Last but not least: game development is not currently something I would recommend to anyone as a career. Yes, there are successful indie developers, but there is a lot of survivorship bias there.
Working for big publishing houses is bad enough that it got Americans to unionize, something I thought we wouldn't see for a long time, and you will have neither the time nor the energy nor the permission to work on personal projects if you ever go there (it might still be a valuable experience though).
Also, the obligatory follow-your-dreams advice: the market is big, and there is usually a niche off the mainstream that is fun to work in, where the relevant people know each other, and while there may not be many jobs going around, there is not too much competition for these jobs either.
For your specific case: If you are interested in computer graphics, it might be interesting for you to visit a Demoparty. Most of these are in Europe, but assuming you are in the US, @party would probably be the best option.