Some of the tournaments are officially rated by the the US Chess Federation (https://www.uschess.org/). The Evanston Scholastic Chess tournaments are intentionally kept as causal and they are not rated by USCF. However, there are many USCF-rated tournaments (both local and nationwide) that are available to you and to your kids.
To participate in a USCF-rated tournament, your kid needs a US Chess membership (https://new.uschess.org/join-us-chess). At the time of writing this article, youth membership costs $24 for a year.
Many Evanston kids participate in the annual Illinois K-8 championship, and many Evanston kids and schools have won several awards in previous IL K-8 tournaments.
The Evanston Chess Club (https://evanstonchess.org/) also runs tournaments; the tournaments are "open to players who are EITHER age 14 and older OR whose US Chess Current Published Regular Rating for the month of the tournament is 900 or higher."
Another local favorite for Evanston kids is the Kumbaya tournaments (typically once a month and typically held at Niles North High School).
Here are two pages where you can find USCF-rated tournaments in IL: