I took off an entire year before my first degree after high school and just took language classes for fun, and it was the best thing I could have done to settle into my undergrad degree when I eventually went. The truth is, people who discourage it tend to do so because they think you will need to play catch up but there is actually nothing to catch up to, its just arbitrary standards about what you should do and when. It will never be too late to do and become the things that you want. But when you are burnt out, and need a mental health break, especially when you have avenues to take a break, you should listen to your body and do it.
How you use your gap semester is up to you, whether its getting more sleep or taking some pottery classes for fun, but I found it fulfilling to have a break where I was not just running on a hamster wheel, worrying myself sick about my miles long to do list. And I was the better for it when I went to uni afterwards, I was more focused and I had a better understanding of what I wanted out of my academic career. So yeah, do it, the refresh is more likely to help than it is to harm, just be balanced in how you use it e.g. do some hobbies now that you aren't beholden to the school schedule, don't jam pack your time away and come back tired etc