no, they’re fundamentally different software with /e/ Parental Control being less capable. At the moment /e/PC isn’t connected or has app-based (or overall) time restrictions, rather app-age-restriction and DNS based blocking by age group. /e/PC doesn’t need another /e/PC device yet to be configured, it’s standalone.
I’d put this into an extra thread. The official (former “stable” release branch) has an Android13 (t) version, you’re on Android 12 (s).