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DerBesserwisser: First things first:

Great update, that brings a lot of convenience into the client !

The thing coming next feels ungratefull but I'll throw it out anyway:

While the jump list is a great thing to have, due to me having the client usually minimized to the tray, I can't get much use of it > if I see the taskbar entry, the client is already open, so using the jump list would practically be more costly (in terms of mouse milage and clicks) than just using the ui.
Would it be possible to have it accessible through right clicking on the tray icon ?

Another thing I think would be good to have is a filter option for the recently played games:

For testing purposes I connected my psn account to galaxy, and now I got an entry for Uncharted in that jump list, which makes no sense (for me) as I can't start it on my computer. No big deal for me as I will disconnect my acount again till the next Galaxy release, buit others might want to keep the integration active.
There are a few ways to access the jump list even if you have the Client minimized to tray: you can pin the Client to taskbar (the icon stays there even if Client is in the tray) or to Start menu and you can access it via Start menu if you search for the Client (e.g. open Start menu and type "galaxy").

Regardless, we do want to improve the tray icon menu at some point :) but I can't say when that will happen.

About filtering: it can be pretty tricky to get it right and make sure it's understandable to the user why certain games don't appear there.
DerBesserwisser: How about placing it in the inegration panel in settings (below each integration), having it active by default (so users can't miss those games, unless they activly try to avoid them) ?
That's one of the possibilities, yes. For now, however, there are other, more important features we need to implement.