Git desktop - why I have Pull origin?

I just did "merge pull request" from my staging to main branch (and then "deployment via git" on server). Everything shows fine on the live site. But why then Pull origin is showed on my staging branch if I just merged from that one to live? I'm afraid to blow-up something. Thank you in advance

So when you look at the history with gitk --all &¹ you should see relatively easily that your staging branch is 14 commits behind the origin/staging branch.

What the tool is suggesting with "pull origin" ² is to bring your local staging branch up to date with the origin/staging branch, and since your local staging branch does not have any un-published local changes this will be a trivial fast-forward merge (in which your local staging branch is just moved forward to the commit origin/staging is pointing to).

Your situation is much simpler than the example I describe in this answer but you might gain some understanding on how multiple updates to a branch from different actors can result in conflicts.

In your case "merge pull request" done by your git server is the another actor and you do not have a conflict, only your local branch is a bit out of date. But sooner of later you will experience this, so in any case it is good to be prepared and I think looking into this aspect will help you decipher your current situation.

¹ And you should use gitk --all & all the time regardless of this issue! No matter what this Git desktop program claims to be and provide, gitk is superior in its features of visualizing, and you should use that as your primary history viewing tool.

² Which I find incredibly imprecise and almost misleading. Git will perform pull operation on a branch and not a remote!