We want to use some encouragement and we decided to draw some small prize among the respondents.
However, for a potential win, we need the person’s email address.

Is it possible to store an email address somehow separately from other responses so that it is not possible to combine the address and responses?

Not within the same survey. However, it is your responsibility to separate personal data from results. This is how things have been handled in market research for years.

However, if you want to separate technologically, then you will have to chain two surveys via the END URL feature and "auto load", with the email address in the second survey.