The TV has become another device. Kid profiles, PIN-locked adult profiles, and turning off autoplay will solve 90% of what parents worry about.
Manage Profiles → Add Profile → Kid. Set the age to the youngest viewer. PIN-lock the adult profiles: Account → Profile Lock → PIN → On.
On a kid profile → Playback settings → Autoplay next episode → Off. Autoplay is the single biggest driver of "ten more minutes" turning into two hours.
Profile → Edit Profiles → Kid Profile. Content is filtered to G/PG by default. Set a PIN on adult profiles: Profile → Parental Controls → Profile PIN.
The TV YouTube app has a separate YouTube Kids option. It's much safer than the main app. For older kids, use the main app with Restricted Mode → On and sign in with their supervised account.
Settings → Parental Controls → Prime Video PIN. Rating restrictions are set per device — repeat on each TV.
Settings → General → Screen Time → Turn On Screen Time → Content & Privacy Restrictions. tvOS uses the same Apple ID, so limits you set on an iPhone can sync here.
Many TVs are always-listening for voice commands. If that unsettles you, turn it off: Settings → Privacy → Voice. Nothing breaks.
Most streaming account areas have a master "Require password for purchases" toggle. Turn it on.