I just bought Airpods Pro 2, are these things normal?

I finally got some Airpods Pro 2 as a birthday gift yesterday (best headphones I’ve ever had in can already tell!) and I have already noticed a few things that make me slightly nervous about them, basically wondering if I am having issues. This Screenshot of my widgets app is before I even touched them in the morning. They are staying connected to my phone even when they have been put back in the case which is odd to me? Shouldn’t it disappear at some point? Another thing is WHY DOES IT SAY THE EARBUDS ARE STILL CHARGING? It makes me nervous that the internal batteries are gonna be overcharged and damaged or something similar. Anyway, are these things normal? This is probably the smallest and most expensive piece of technology I’ve gotten so I want to make sure it’s in working order and I shouldn’t immediately use the AppleCare I got with them.

I finally got some Airpods Pro 2 as a birthday gift yesterday (best headphones I’ve ever had in can already tell!) and I have already noticed a few things that make me slightly nervous about them, basically wondering if I am having issues. This Screenshot of my widgets app is before I even touched them in the morning. They are staying connected to my phone even when they have been put back in the case which is odd to me? Shouldn’t it disappear at some point? Another thing is WHY DOES IT SAY THE EARBUDS ARE STILL CHARGING? It makes me nervous that the internal batteries are gonna be overcharged and damaged or something similar. Anyway, are these things normal? This is probably the smallest and most expensive piece of technology I’ve gotten so I want to make sure it’s in working order and I shouldn’t immediately use the AppleCare I got with them.