Line 17 of the script is the function that sets up the path:
I don’t know where and how the path needs to be set up for Windows, or if Scrivener on windows even needs this to be done; perhaps it runs with the path already set up. The path is required so that Scrivener can find Quarto and the other bits, but that may work better on Windows than macOS, I just don’t know. You can download just that script and run it from the windows terminal with a sample markdown file to see if it works, as I said each bit can be broken down and tested bit by bit.
As long as Scrivener-windows is broadly similar to Scrivener-mac, then the project template should be set up with the compile format and everything ready to go. Sometimes you may need to check the Compile Layouts are all assigned. But, here for example, I’ve added the project template anew and created a shiny new project, then just hit compile and this is what I see:
The project is compiling to Multimarkdown, has four project formats and the PDF one is already selected, the Section Layouts are all assigned, the front matter is correctly assigned to the Metadata document. You do need to make changes to paths and fonts in Metadata as there are absolute paths that are required and font names like Alegreya that are specific to my system.
Now where Windows used to be different was some limitations around post-processing (is that still the case, I don’t know?):
On macOS the Ruby script is embedded in the project format, with the arguments specified. Now &> is used to redirect all errors and output to a log file and I doubt &> works on Windows unless you are using cygwin / msys2 / WSL? This may need a tweak?
The top level view then is: the project template should take care of all the details, it is set up to Multimarkdown[pandoc syntax] output with all the Section Layouts, Styles etc. all wired up. The embedded post-processing script takes the Pandoc-flavoured markdown output from Scrivener, and rewrites it (so e.g. Output.md that Scrivener produces is copied to Output2.qmd, the original is left in place so you can check differences etc.), then runs Quarto on Output2.qmd.
Platform differences may break some of those wires
What happens if instead of the project zip, you use the project template (make sure the file name ends in .scrivtemplate, some browsers may append .txt etc.):
As I know it the project template contains the compile formats. Indeed these should also have been visible when you just opened the .scriv project. If you browser to Quarto.scriv/Settings/Compile formats/ they are there.
I don’t know why they do not show in Scrivener. You may get better traction asking other windows users, they will be better able to contend with what appear to be platform variances.
I can report that bug then, I imported the template, I did File-> New project->options, import template->Non fiction->Scrivener+Quarto and then after I click the create project button, nothing happens, not sure what to do as this is a custom template, is there support for this kind of things ? Thanks so much @nontroppo so far for the help !
A major release with a lot of small changes, there is no blog post yet, but the changelog is here:
There are some nice updates for Typst support, in fact the Quarto developers made upstream changes to Pandoc to support the use of CSS properties that can convert to Typst code, here is an example for nice styling of tables (which many quarto plugins generate):
The Quarto developers are working to get their Typst support to be good (or better as in the case of the Typst-CSS tools above) as their TeX support, which will be great as Typst is much faster, much smaller, and much simpler for PDF generation.
Metadata document. You do need to make changes to paths and fonts in 
