The web app doesn’t support gapless playback. Some albums are just one long continuous stream of sound, with no gaps in-between songs. The web app forces small pauses between songs, which is annoying when listening to such albums. Also, the keyboard’s media keys might not work with the web app. And, if you are an audiophile, you might care about bit-perfect playback. Using a browser doesn’t guarantee that, but I don’t know if you get that with the desktop app either, when used with Wine.

Not entirely sure what MPRIS is, but the Qobuz app does respond to media keys (Play/Pause, Next, etc.) of my keyboard under KDE.

Browser is fine as long as you don’t need gapless playback.

Their Windows app works just fine with Wine. Requires some tinkering to make it work, though.

https://appdb.winehq.org/objectManager.php?sClass=version&iId=42813