It is the second time my chrome apps on various machines (windows and linux) get infected.

Clearly it happens through extensions since I synchronize all my chromes.

Now I got the shopping deals malware, when on linux I see that the extension manager is disabled, clicking on it carries me tot he shopping deals page.

First of all I wish to understand if they may have compromised my linux system as well.

Also I would like to make it clear that their redirection bring me to a zalando shop I wonder if such chain lowers itself to such methods or if it is just a trick to infect the machine even deeper.

Second I ask myself why chrome is so weak, I usually choose opera or firefox but chrome is the only one I can use with netflix.

i don't think your system is corrupt, but maybe the malware got a good look inside.
tbh, i don't know how safe chrome's sandboxing is.
a deeper system analysis would be required to get some answers.

in any case, any browser is only as safe as the finger doing the clicking.

remove the extensions, start with a clean profile (remove the folders).

be more careful in the future.

maybe don't sync at all, or try to restrict it to bookmarks?

personally, i still prefer firefox because a) it isn't google and b) it has some nice security addons that just aren't available for chrom/e/ium.

Try new browser profiles for a day or two?

Contact zalando's marketing department and make them aware of this. If they're not scum they ought to do something about it -- if they are scum then go to somewhere like theregister.co.uk and let them know so that they can let the world know.
As for the current issue I suggest just not synchronising your Google Chrome on your PC (I would suggest not doing it on any device but that's jut me being that silly and wanting privacy and being cautious.). Delete the google-chrome directory in ~.config then never log into Google again.

Edit: I, too, use Google Chrome for Netflix (though I keep meaning to try Firefox again so thanks for the reminder) but just make sure it's all I ever use it for since Google are pretty clear that they don't care about privacy and are all about advertising.