Web Search Apple Watch Family Setup

Sed the "Set Content & Privacy Restrictions" or "Prevent web content" sections in:

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

I have two Apple Watch SE (one each for two of our kids). One works fine to browse web content (our older child discovered they could browse links from Messages or Mail and now sends our younger child messages with URLs embedded to browse for themselves, which in turn taunts our younger child whose watch just loads blank pages for the same URLs that work fine on the older one's watch).

Via Apple Family Setup, the settings to control the paired childs' watches to my iPhone are controlled via Screen Time on my iPhone. I have both of them's "Web Content" set to "Limit Adult Websites". Both have "Siri: Web Search Content" set to "Allow". What other restrictions are there that I need to verify to have the younger one's watch be able to browse the web?

I've had our older child's iCloud account logged into an iPhone 4S just to monitor their chat history via iCloud and our younger one only has their iCloud account assigned to their Apple Watch. They don't have an iOS or MacOS account set with their Apple ID/iCloud account.

This is not an option under Family Setup for Apple Watch. I just upgraded both Apple Watch SE to watchOS7.3 hoping it would resolve the issue for our younger child - so he could browse websites from Messages or Mail on his Apple Watch and it still fails to load sites. It attempts; the progress bar makes it about 1/4 of the way across and then it stops and the watch face remains black with the URL at the top.