Biblatex: article with two printed references section, plus citing after

I have an article which must have two references section. I used biblatex to do that. In order for the numbered references to continue from one section to the next, I enabled the global option defernumbers=true, and used resetnumbers=false for the second reference section.

I also have a third section, with citations that have already appeared in the first or second reference sections. Here’s an MWE:

documentclass{article}

usepackage[defernumbers=true]{biblatex}
usepackage{hyperref}

begin{filecontents*}{mwe.bib}
@misc{paper1,
    author={name1},
    title={title1},
    year={2021}
}

@misc{paper2,
    author={name2},
    title={title2},
    year={2021}
}

@misc{paper3,
    author={name3},
    title={title3},
    year={2021}
}
end{filecontents*}

addbibresource{mwe.bib}

begin{document}

begin{refsection}
section{Section One}
Section one citations: cite{paper1,paper2}
printbibliography
end{refsection}

begin{refsection}
section{Section Two}
Section two citations: cite{paper3}
printbibliography[resetnumbers=false]
end{refsection}

section{Section Three}
Second three citations: cite{paper2}

end{document}

The rendered PDF is shown below:

My questions are:

1. Why the second reference section starts numbering from 1 rather than 3? (Note defernumbers=true and resetnumbers=false, and I cleared every temporary file like .aux and recompiled multiple times.)
2. How to make the citation in the third section to appear correctly?

Edit: This is what I want to achieve (differences from the above image are depicted in red):

documentclass{article}

usepackage[defernumbers=true]{biblatex}
usepackage{hyperref}

defbibfilter{notsegmentOne}{not segment=1}

begin{filecontents*}{jobname.bib}
@misc{paper1,
  author = {name1},
  title  = {title1},
  year   = {2021},
}
@misc{paper2,
  author = {name2},
  title  = {title2},
  year   = {2021},
}
@misc{paper3,
  author = {name3},
  title  = {title3},
  year   = {2021},
}
end{filecontents*}
addbibresource{jobname.bib}

begin{document}

section{Section One}
Section one citations: cite{paper1,paper2}
printbibliography[filter=notsegmentOne]

begin{refsegment}
section{Section Two}
Section two citations: cite{paper3}
printbibliography[segment=1]
end{refsegment}

section{Section Three}
Second three citations: cite{paper2}

end{document}