Earlier quoted context omitted.
No, it's public and has been run for 11 years already and will continue to do so in foreseeable future. I would say it is the most popular one in my home country and it has good reputation among users. From my experience most linkrot issues comes from the fact that sites and documents URL shorteners link to go down before URL shorteners themselves. Many websites from 11 years ago doesn't exist anymore.
Will you die, will your heirs continue to operate this service? Or do consequences beyond your life not concern you? (e.g. "Why should I care about climate change, I'll be dead before it gets bad!" ) To mitigate the harm you've already caused, you should put the service into a read-only mode and contact Archive Team about handing off the database. You should do this today, before you get hit by a bus.
And I care about climate change, even after my death.