Explaining a gap after caregiving or layoff - first time posting

I have been out of work for 2 months and worry about the gap. This is my first time dealing with any of this. I am not sure how much to explain. What do you say in interviews?

I listed the volunteering and course under the same dates and kept the explanation to a sentence in the cover letter.

I was hired after a 2-month gap. The manager said the skills test mattered more than the dates.