I don't see an Airplay button in Safari when viewing videos on websites on iPad or iPhone

When I'm viewing a video on a website in Safari on any of my three mobile devices, I don't see an Airplay button in Safari. I have no problem streaming these videos to my smart TV by turning on Screen Mirroring from Control Panel, but I expected to be able to do this directly from an Airplay button in Safari.

Use AirPlay to stream video or mirror the screen of your iPhone or iPad - Apple Support

This article says:

Tap the AirPlay button. In some apps, you might need to tap a different button first. For example, in the Photos app, tap the Share button, then tap the AirPlay button.

It doesn't quite tell you if Safari is one of the apps where you'll find an AirPlay button. Unless I'm wrong, it's not, and you have to use Screen Mirroring. Any help would be appreciated.