PS3 needs long warm-up before it can read game disks

You most likely need to replace the blu-ray lens laser in your PS3. If it's reading DVD's and regular CD's fine, but it only affects bluray games and movies. It's the laser.

The PS3 is a 10+ year old system and many of them go bad due to use. I've fixed a bunch of these at my repair shop before and what happens is the blue light on the lens just doesn't light up if you opened up your PS3 and observe the disc spinning while being read. To detect the DVD and CD lasers, you can use your phone camera and view the invisible infrared laser shown on the spinning disc to verify.

The laser looks like this:

The repair is a bit tricky if you've never opened up a PS3 before as there are a bunch of screws and flex cables you need to loosen. Otherwise you can just follow a Youtube tutorial.