Problem installing StanHeaders and rstan in Github actions

I have a standard Github action for publishing a Quarto blog. It automatically installs package dependencies using renv, and all other packages install fine, but for some reason it is failing with StanHeaders (log below). I suspect it is for the same reasons as #964 - the stan_math git submodule doesn't get downloaded.

The only thing I can think of is to specify the last version on CRAN to be installed, rather than using "https://stan-dev.r-universe.dev", but that is quite outdated.

Any alternative ideas about how to solve this?

Error: Error: Error installing package 'StanHeaders':
=======================================

* installing *source* package ‘StanHeaders’ ...
** this is package ‘StanHeaders’ version ‘2.36.0.9000’
** using staged installation
cp: cannot stat 'inst/include/upstream/src': No such file or directory
cp: cannot stat 'inst/include/upstream/lib/stan_math': No such file or directory
cp: cannot stat 'inst/include/upstream/lib/stan_math/stan': No such file or directory
cp: cannot stat 'inst/include/upstream/lib/stan_math/lib/sundials_*': No such file or directory
cp: cannot stat 'inst/include/upstream/lib/stan_math/lib/sundials_*/include/*': No such file or directory
cp: cannot stat 'inst/include/upstream/lib/stan_math/lib/sundials_*/src/*': No such file or directory
** libs
using C compiler: ‘gcc (Ubuntu 13.3.0-6ubuntu2~24.04) 13.3.0’
using C++ compiler: ‘g++ (Ubuntu 13.3.0-6ubuntu2~24.04) 13.3.0’
using C++17
make: *** No rule to make target 'nvector/serial/nvector_serial.o', needed by 'static'.  Stop.
ERROR: compilation failed for package ‘StanHeaders’
* removing ‘/home/runner/work/venpopov.github.io/venpopov.github.io/renv/staging/1/StanHeaders’
install of package 'StanHeaders' failed [error code 1]
- Installing StanHeaders ...                    FAILED
Traceback (most recent calls last):
13: renv::restore()
12: renv_restore_run_actions(project, diff, current, lockfile, rebuild)
11: renv_install_impl(records)
10: renv_install_staged(records)
 9: renv_install_default(records)
 8: handler(package, renv_install_package(record))
 7: renv_install_package(record)
 6: withCallingHandlers(renv_install_package_impl(record), error = function(e) writef("FAILED"))
 5: renv_install_package_impl(record)
 4: r_cmd_install(package, path)
 3: r_exec_error(package, output, "install", status)
 2: abort(all)
 1: stop(fallback)
Execution halted
Error: Process completed with exit code 1.

Start with .github/workflows/publish.yml and the renv::restore() step that installs StanHeaders. Compare the missing stan_math paths and submodule behavior with issue #964, then reproduce the failure using the provided GitHub Actions setup. Done means StanHeaders and rstan install successfully in the workflow without relying on an outdated package version.