I would not say "rest on the street". We say "In the street." Don't play in the street. I only say "on the street" when talking about the location of a house or building. My house is on that street. But for moving objects, I say "in the street." I hit report, but I am curious if anyone else says this phrase the same as I do or not. To me, the English here sounds unnatural, and it is my native language
I'm the same, but there are some regional differences. I'd say "Don't play in the street" but "Don't play on the road".
To anyone who thinks "in the street" is incorrect, here's that famous duet by Mick Jagger and David Bowie - Dancing in the Street https://youtu.be/x4rzCzV8qjM. (Sorry, I mean Sir Mick Jagger.)