I tend to go with what I was taught and avoid contractions in professional writing.

You may use contractions. It can seem very stilted in our day to use: cannot, will not, should not. It does depend on the country - perhaps some non English -speaking countries when using written English might prefer that. However, we are generally quite relaxed.

Hello, To be safe, I would not use contractions in your formal emails. The work culture and formality of emails can depend on the job or internship. Some companies would be fine with contractions, but others would expect formal English without contractions. I would be conservative in your case and refrain from using them, at least for now. If you see in several emails from management or other “higher ups” in the company that they are using contractions, then perhaps you could use them a bit more.