Battle Pass
Pass quests are the same on every device
Quests are stored on the server: the same on computer and phone, and the server counts PvP wins and levels.
Battle Pass quests are now stored on the server: the same quests, progress and swaps on your computer and your phone. Clearing the browser no longer brings completed quests back.
PvP wins in 1v1 arena, team arena and battlegrounds are counted by the server, and the quest line updates right after the fight. The Reach level 50 quest now advances with your hero level, and enemies in dungeons and raids count towards the Defeat N enemies quests.