Btukfyl

Unfortunately all information I can find is merely for macOS or Linux and I haven't been able to translate the solutions to my Windows 10 system.

I'm trying to set up LaTeX in VS Code on Windows 10 but I keep getting:

latexmk: The script engine could not be found.

latexmk: Data: scriptEngine="perl.exe", scriptName="latexmk"

I installed the LaTeX Workshop extension for VS Code as well as TeX Live and C:texlive2018binwin32 is part of my PATH environment variable.

In order to use LaTeX Workshop in VS Code on Windows you need to download and install Perl. After downloading and installing the extension should be able to compile your document. You might also need to then install the latexmk package, but I am not sure.

I personally have Strawberry Perl installed on my PC, but Active Perl should work just as well for this.

In the link you posted titled "information" following the answer given by K. Paul should solve your problem in Windows.

Your first link is the correct one for windows but unfortunately as often happens was hijacked by other users populist answers and then it snowballs so you can't see the key bits of advise.

Heini is describing MiKTeX but his comments would apply to Tex Live. That is you don't need to download Perl or Latexmk as such since TeX Live includes Perl and Latexmk especially since you are finding they may interfere with what should be simple basic compilation runs.

EQUALLY IGNORE his reference to download anything else such as his suggestion for synctex 1) it is already built into tex live 2) there is an issue with windows workshop extension and synctex that's undergoing current changes so lets wait.

Presuming you are at a command line (Cortana task bar = C + enter or WIN+C+Enter)

To check where Perl should be run> where /r perl and the response should be something like

c:texlive2018tlpkgtlperlbinperl.exe

So to call Perl you should have that bin directory early on path as well as the main bin.

Back to your question VS Code is an IDE so edit and save the u14.TeX

TeX Live is a suite of compilers and make commands so you can run say >
PdfLaTeX "c:UserschrisDownloadsu14.tex"

and presuming no errors makes "c:UserschrisDownloadsu14.pdf" simples

Back to your problem Latexmk tries to run several passes of the make comands in effect it is a script kiddie on caffeine and employs the Perl environment to run in so first test is ignore it and check you can manually run pdfLaTeX on your file as above proving that Tex Live is not an issue. now try at cmd>

pdflatex -synctex=1 -interaction=nonstopmode -file-line-error -recorder -output-directory="c:/Users/chris/Downloads" "c:UserschrisDownloadsu14.tex"

That is what latexmk is trying to "shell" out to and if it does not work at the command line the errors should be relayed to you by latexmk

Depending on your variant of TeX Live you should have the default editor (TeXworks) installed at c:texlive2018tlpkgtexworkstexworks.exe which is a native TeX editor with PDF viewer and can be used for comparison purposes to check fairly complex TeX compilations.

One way to avoid using latexmk should be to have the compilation directives at the start of the tex file(s) so in this case the first line of u14.tex would be.

% !TEX options = -synctex=1 -interaction=nonstopmode -file-line-error "%DOC%"

note that does NOT include the latexmk -recorder option and that may be why you are having an issue see latexmk -recorder doesn't find .fls file containing pdflatex process ID in its name