It's not expected (or remotely possible!) to be perfectly up-to-date on everything being published, but some active effort is better than none.
It's crucial to keep up-to-date with the academic literature. Generally, it is recommended that you set up a Google Scholar alert for authors and keywords related to your research. You may also consider subscribing to a journal's RSS feed with an RSS reader app. Reeder seems to be a popular tool for Apple products.
For literature searches on previously published work:
Explore the literature through citation networks via tools like ResearchRabbit. Even more simply, use Google Scholar to see which papers cite a paper of interest and use that to broaden your search.
Run queries on Perplexity (use your Princeton email) and check out the sources that Perplexity relies on to answer your question.
Remote Access
The easiest way to access journal articles off-campus: