I also noticed that the app is actually listed 4 times (!) when I try to open some file and I choose "Open with" -> "Other application":
Why is it happening and how to fix it?
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There were 2 things that I did to solve this issue.
First, thanks to @KGIII I removed Applications menu entries using App Editor. I found out that the "duplicats" were actually Nautilus file manager, and not the Pantheon Files.
Then I just removed Nautilus from my system using
apt purge nautilus.
Now, I do not have any "duplicates" in both the Applications menu and the "Open with" menu.
The only thing that I would like to learn is how Nautilus was installed on my system. I did not install it explicitly by myself, I think it had to come in as a dependency of some other package. However, am I able to know for sure how it got installed?