I don’t mean to say that you’re completely wrong in your reasoning, but grammatically speaking, we use have + verb in past participle which we call present perfect no matter what verb is used.

In this case, you’re talking about something you’ve experienced, so the correct way would be “I’ve run” (as the past participle of run is run).

If you’d like to take a detailed look at it, here you have: Present Perfect - British Council and Using “have ran” or “have run”.

Btw, It’s completely normal to make mistakes! We’re all human, and part of being human is learning and growing from our errors.

We’ve been mishearing him, it’s fee speech absolutist.