The Sesame Street deal with HBO Max was for first-run shows. After they air on Max, they're available on PBS. The morning block on most PBS stations is called PBS Kids. They run a number of kids shows, including Sesame Street. I imagine any deal Sesame Street makes after Max will also include PBS in some way. PBS Kids is also available as a streaming channel and a YouTube channel.
Watch your favorite PBS KIDS shows on the 24/7 LIVE TV stream!
pbskids.org
If you click on the link, go to videos, and you'll be able to watch Sesame Street videos.
They continue the linear broadcast of Kids for families that don't have access to internet, cable, or other pay TV services. That's part of the budget, and why public TV receives a congressional appropriation.