Hello
I activated the third party repository in gnome software and after restarting I activated the chrome repo and installed chrome with rpm-ostree.
Do I get the updates automatically with this method?
Yes, if you have automatic uodates enabled in Gnome Software, it will update it for you, or you can use rpm-ostree update in command line.
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I am surprised because I have not found this method in any of the articles.
Thanks for the info 
I believe that automatic updates at Gnome Software only works with Flatpak. As far I know, ostree doens’t automatic update via Gnome Software.
Software will update rpm-ostree as well, depending on if the particular package is reachable at configured repos.
Gnome Software can update system using rpm-ostree and can even do a full rebase, you will see an option to upgrade to Fedora 33 in Gnome Software on Tuesday, when Fedora 33 will be released. If you confirm, Gnome Software will do a full rebase using rpm-ostree under the hood.
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I’m talking about “Automatic Updates” option at Gnome Software.
At my machine, at least, it never auto-updates ostree (aka gets and installs a new deployment).
I always need to explicitly order Gnome Software to apply an ostree deployment.
There is some talking about this at: https://github.com/fedora-silverblue/issue-tracker/issues/87.