Hello again,
I tried chromo and edge browser in 2 different pc, logged in steam in another pc & mac still same it does not work. And the EA play page does not even load on mobile devices trough steam app.
Personal observation:
1.I have also given a screenshot between a star wars game and crysis steam's store page. I have a hunch the EA play add to library button is connected to the steam store page add to library which does not exist for these 3 games. Also for every game still can be bought on steam and is in EA play has a special line called included on your EA play pass and a "Play Now Button".
2.For star was squadron you can see I can buy the game and also add it to library and for crysis it says this game is no longer being sold on steam and no add to library option and also it is same for MOH airborne and Titanfall.
3. Maybe Ea play store add to library button button just redirects to store page add library button which does not exist for those 3 titles.