can parents view their childs messages through screentime

No.

The method used is to actually look on the child’s phone; so you need to ensure continued physical and logical access to your child’s phone.

The ability of your child to alter or change his/her account and passcode/password should be inhibited w/ a “known only to adult” screen time password configured after selecting “This is a Child’s Phone” on the screen.

Use parental controls on your child's iPhone, iPad, and iPod touch - Apple Support

The child’s AppleID also should have been setup as described below to help ensure that all Parental Control features work as intended.

Create an Apple ID for your child - Apple Support

I do not believe that is possible. Apple is pretty serious about privacy, even for children. If you want to see their messages, ask then to show you.