Most responsive design is based on screen dimensions with CSS media queries these days, not on the actual class of device.

The server now needs to respond with the Accept-CH header specifying it wants the client to send the mobile client header by including the "UA-Mobile" value. A compliant client will then send the Sec-CH-UA-Mobile header in its next request with either the value "?0" or "?1".

The modern solution is to use CSS with media queries. You tell the client how the site is supposed to look on various screen sizes. The client applies the rules without leaking any information about which rules it chose to apply.

That's mostly done client-side these days; having the server treat clients differently doesn't happen as much anymore.

I think media queries have been the way to do that for awhile. Or I think there's some javascript trick to do it.