Kenmore microwave turns on when door closed

Have the original Kenmore microwave that was installed in our home, when it was built in 1997.

Yesterday, I noticed when closing the microwave door, after removing food, that the lights inside turned on, and the noises that I hear while cooking food (sounds like a fan maybe?) come on for 3-4 seconds after the door is closed ,then the sound goes away and the lights turn out.

It didn’t do this before.

Wondering if perhaps I have a bad door switch, or something worse?

Is this worth repairing myself? Seems a new $200 microwave from Lowes has more bells and whistles… of course, this one suits us just fine for what we are doing…