Share Across Devices applies within the SAME Apple Account, i.e., to devices signed into the same account. It does not apply to devices in a Family Sharing group signed into different accounts.
For example, I see it on my Mac when the Family Member is set to me.

Turning ON the Share Across Devices setting would mean any change I make to Screen Time settings on any device – either of my two Macs, my iPad Pro or my iPhone, would apply to all of those devices (and to my Apple Watch). With it OFF, I can change the setting on a device and that change applies only to that device.
When I set the Family Member to one of my children, the Share Across Devices setting is not shown, as intended.
More info from Apple:
Set up Screen Time for yourself on iPhone - Apple Support
Use Screen Time to manage your child's iPhone or iPad - Apple Support
More details:
- Why the option is missing: Apple changed how Screen Time and Family Sharing sync in newer OS versions. Under the updated Family Sharing and Screen Time framework, restrictions and app limits imposed on a child's account via Family Sharing are designed to apply globally to their Apple ID across all signed-in devices rather than being independently toggleable per device via a "Share Across Devices" master switch.
- Why Safari now blocks on the Mac too: Because restrictions applied to a child's account through Family Sharing now synchronize natively across their devices tied to that Apple ID, disabling Safari on the iPhone simultaneously disables it on the Mac profile.