31M - How does Prednisone work so far past its elimination half-life?

I'm used to psychiatric drugs where how long the drug works is proportional to its elimination half-life. For example, a psychiatric drug that has a half-life of 4 hours would work noticably for like 4-ish hours and then when it stops working noticably you have to take another to notice the effect again.

That being said, Prednisone has an elimination half-life of 3 to 4 hours, but my mom only takes it once a day for her auto-immune condition. AI said that it breaks down into methylprednisolone but that has an elimination half-life of 1.8–2.6 hours so I still don't see how it can last an entire day.

How does Prednisone work so far past its elimination half-life?