Works for me on my Pixel phone, both with deezer playlists and my own.

My playlists I can start by tapping the shuffle icon, with deezer playlists I tap the shuffle icon on the now playing pane and start the playlist, or start the playlist and tap the shuffle icon in the now playing pane.

There is no shuffle option on my android app. I've attached a screenshot fyi

Hi ​@Julie L !

Start play first song   tap in red area to open

tap on two arrows  turn ON shuffle