Harvard-style citation: "and" in running text but "&" in parentheses

Your formatting requirement is best handled by switching from the natbib citation management package to the apacite package (with option natbibapa, so that you can keep using citet and citep) and from the agsm bib style to the apacite bib style.

documentclass{article}
begin{filecontents}[overwrite]{references.bib}
@article{li2020most,
    author  = {Li, Ming and Wang, Qiang},
    title   = {The most important paper of the century},
    journal = {Journal of Nonexistence},
    volume  = {25},
    number  = {4},
    pages   = {250--251},
    year    = {2020},
}
end{filecontents}

%usepackage[longnamesfirst]{natbib}
%bibliographystyle{agsm}
usepackage[natbibapa]{apacite}
bibliographystyle{apacite}

begin{document}
citet{li2020most}, citep{li2020most}.
bibliography{references}
end{document}

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Addendum to address the OP's follow-up question. The OP has indicated that his/her publisher has a separate formatting requirement which may be violated by the approach suggested above. To meet the publisher's supplemental requirement, I suggest one should proceed as follows:

• Find the file apacite.sty in your TeX distribution. Make a copy of this file and call the copy, say apacite-natbibapa-nosort.sty. (The reason for this choice of name will become apparent soon.)

• Open the file apacite-natbibapa-nosort.sty in text editor; the program you use to edit your tex files will do fine.

• On line 46, change

  ProvidesPackage{apacite} 
  

  to

  ProvidesPackage{apacite-natbibapa-nosort} 
  

• Change all three instances of the string

  [longnamesfirst,sort]
  

  to

  [longnamesfirst]
  

  i.e., delete the 'sort' option. In my copy of the file, the strings occur on lines 998, 1000, and 1002.

• Save the file apacite-natbibapa-nosort.sty to the directory that contains your main tex file.

• In your main tex file, be sure to include the instructions

  usepackage[natbibapa]{apacite-natbibapa-nosort}
  bibliographystyle{apacite}
  

  in the preamble.

Happy BibTeXing.