Does SJPP have slow days and busy days?

It also depends on when you head out. You can enjoy a very quiet SJPdP on pretty much any day of the week if you begin your Camino in January or early February..
If you are afraid of crowds, Winter would be best, or try a quieter Camino maybe.

I thought about this very question before my first Camino. The consensus seems to be Friday, Saturday, and Sunday are busier than the others. I left on a Tuesday. I have come to realize that this is, as the Brits call it, a mug's game. Leaving on Tuesday drops you into Pamplona on Friday (I stopped at Orisson), and you have then a "peak" day for people that start in Pamplona. Eight or ten days later, you have either just missed, or just hit, another group that starts at Logrono. If missing peaks is your goal, the only one to consider seriously is Sarria, where you do not want to stop on a weekend. Speed up or slow down as you go, or even better, delay yourself a day or two with the very worthwhile side trip to Samos....

Buen Camino

If you take your overnight stay in Orisson on the first day, starting in the afternoon is an option. I left Saint Jean Pied de Port at 1:30 pm and I was alone in the world.

In general: people tend to work their week till the end, and travel to- and start their camino during the weekends. So in general, in weekends the numbers are higher from any bigger starting point on the camino.
So tuesday till thursday are about the lowest days, also in SJPdP