I decided to give them a chance after an in-person interview. It's been about a year, and they still haven’t completed a single task in Jira.

A year is a very long time for them to improve and you have given them enough time to change.

So I would just let them go right now.

I started meeting with them daily, but it turned into an exercise in testing my patience.

No hire is better than a bad hire. You will not get back that time and money you spent on that intern. Are you willing to invest more time on to someone that still cannot complete any task after hiring them a year later?

If the answer is still No, fire them right now.