biblatex: continuous reference numbering without duplication

I am using the refsegment feature of biblatex to assemble multiple bibliographies within the same document. I would like to have continuous reference numbering across the refsegments (i.e., if the last new reference of refsegment N is assigned the number i, then the first new reference of refsegment N+1 will be assigned the number i+1). I would also like to avoid duplication of already-cited references in the sub-bibliographies. That is to say, while a given reference may be cited in more than one refsegment, it should be included only in the sub-bibliography for the refsegment in which it first occurs. Here is a simple example:

refsegment #1:
The quick brown fox [1] jumps over the lazy dog [2].
Bibliography:
   [1] Fox reference.
   [2] Dog reference.

refsegment #2:
The lazy dog [2] was busy doing nothing [3].
Bibliography:
   [3] Reference on nothing.

Note that reference #2 was not included in the second bibliography even though it was cited in the second refsegment because it had already been included in the first bibliography.

This post proposed a solution to this problem, namely the onlynew bibliographic check, which suppresses repeated bibliographic items. The proposed solution keeps a running tally of bibliographic items (stored in the control sequence blx@entrycount) and records the next reference number at the start of each refsegment (in the control sequence blx@entrycount@thec@refsegment). Then, if the number assigned to a given bibliographic item (thefield{labelnumber}) is less than (ifnumless{}) the latter quantity, it is skipped in the bibliography (since it has already been referenced). However, upon compilation (TeX Live 2019), all citations are assigned the number zero, the bibliographies are empty, and the following warning is emitted:

LaTeX Warning: Empty bibliography on input line <n>

The below example reproduces the problem. What changes are needed to fix the code in the MWE?

---

MWE (adapted from linked post):

documentclass{article}
usepackage[defernumbers=true]{biblatex}
usepackage{filecontents}

makeatletter
% Overall entry counter
csnumgdef{blx@entrycount}{0}
AtEveryBibitem{%
  csnumgdef{blx@entrycount}{csuse{blx@entrycount}+1}}

% Continued from this label number
appto{newrefsegment}{%
  csnumgdef{blx@entrycount@thec@refsegment}{csuse{blx@entrycount}+1}}

% Skip entries with label numbers less than the continued number
defbibcheck{onlynew}{%
  ifnumless{thefield{labelnumber}}{csuse{blx@entrycount@thec@refsegment}}
    {skipentry}
    {}}
makeatother

begin{filecontents}{jobname.bib}
@Book{companion,
  author = {Goossens, Michel and Mittelbach, Frank and Samarin, Alexander},
  title = {The LaTeX Companion},
  edition = {1},
  publisher = {Addison-Wesley},
  location = {Reading, Mass.},
  date = {1994}}
@Article{gillies,
  author = {Gillies, Alexander},
  title = {Herder and the Preparation of Goethe's Idea of World Literature},
  journaltitle = {Publications of the English Goethe Society},
  volume = {9},
  date = {1933},
  pages = {46--67}}
@Article{bertram,
  author = {Bertram, Aaron and Wentworth, Richard},
  title = {Gromov invariants for holomorphic maps on Riemann surfaces},
  journaltitle = {J.~Amer. Math. Soc.},
  volume = {9},
  number = {2},
  date = {1996},
  pages = {529--571}}
@Book{poetics,
  author = {Aristotle},
  editor = {Lucas, D. W.},
  title = {Poetics},
  series = {Clarendon Aristotle},
  publisher = {Clarendon Press},
  location = {Oxford},
  date = {1968}}
@Book{rhetoric,
  author = {Aristotle},
  editor = {Cope, Edward Meredith},
  commentator = {Cope, Edward Meredith},
  title = {The Rhetoric of Aristotle with a commentary by the late Edward Meredith Cope},
  volumes = {3},
  publisher = {Cambridge University Press},
  date = {1877}}
end{filecontents}

addbibresource{jobname.bib}

begin{document}

newrefsegment
refsegment therefsegment:
cite{companion,rhetoric}
printbibliography[segment=therefsegment,check=onlynew]

newrefsegment
refsegment therefsegment:
cite{companion,bertram,poetics}
printbibliography[segment=therefsegment,check=onlynew]

newrefsegment
refsegment therefsegment:
cite{companion,bertram,gillies,rhetoric}
printbibliography[segment=therefsegment,check=onlynew]

end{document}

Compilation: pdflatex && biber && pdflatex && pdflatex

Output:

documentclass{article}
usepackage[defernumbers=true]{biblatex}

makeatletter
AtEveryCitekey{%
  ifcsundef{blx@entry@refsegment@thec@refsection @thefield{entrykey}}
    {csnumgdef{blx@entry@refsegment@thec@refsection @thefield{entrykey}}{thec@refsegment}}
    {}}
defbibcheck{onlynew}{%
  ifnumless{0csuse{blx@entry@refsegment@thec@refsection @thefield{entrykey}}}{thec@refsegment}
    {skipentry}
    {}}
makeatother

addbibresource{biblatex-examples.bib}

begin{document}
newrefsegment
refsegment therefsegment:
cite{sigfridsson,worman}
printbibliography[segment=therefsegment,check=onlynew]

newrefsegment
refsegment therefsegment:
cite{sigfridsson,geer,nussbaum}
printbibliography[segment=therefsegment,check=onlynew]

newrefsegment
refsegment therefsegment:
cite{sigfridsson,geer,pines,worman}
printbibliography[segment=therefsegment,check=onlynew]
end{document}

documentclass{article}
usepackage[defernumbers=true]{biblatex}

makeatletter
AtEveryEntrykey{%
  ifcsundef{blx@entry@refsegment@thec@refsection @#1}
    {csnumgdef{blx@entry@refsegment@thec@refsection @#1}{thec@refsegment}}
    {}}
  {}{}

defbibcheck{onlynew}{%
  ifnumless{0csuse{blx@entry@refsegment@thec@refsection @thefield{entrykey}}}{thec@refsegment}
    {skipentry}
    {}}
makeatother

addbibresource{biblatex-examples.bib}

begin{document}
newrefsegment
refsegment therefsegment:
cite{sigfridsson,worman}
printbibliography[segment=therefsegment,check=onlynew]

newrefsegment
refsegment therefsegment:
cite{sigfridsson,geer,nussbaum}nocite{knuth:ct:a}
printbibliography[segment=therefsegment,check=onlynew]

newrefsegment
refsegment therefsegment:
cite{sigfridsson,geer,pines,worman}nocite{knuth:ct:a,knuth:ct:b}
printbibliography[segment=therefsegment,check=onlynew]
end{document}