Thanks @technocrat for the inputs!
Here are some precisions.
This is not more true. See release note of version 0.26 https://github.com/yihui/tinytex/releases/tag/v0.26
This issue does not me the AppVeyor channel is broke. It was just an issue with GHA to install TinyTeX binary using r-lib/action/setup-tinytex that is using the install-bin-windows.bat. From what I understand of the above, it should not be related.
Regarging TinyTeX installation
With the last version of tinytex (the R package), we improved the way user can install TinyTeX (the TeX distribution). There is now a specific repo for the binaries
Binaries for OSx, Linux and Windows are available for download as a github release. There 3 binaries for each OS based on how many TeX packages are preinstall. Those binaries can be installed using different methods like using R (for R user) or not (for non R user mainly).
Now you can directly use tinytex::install_tinytex(). It will install the recommended binary for R Markdown which is TinyTeX-1. You can select the version - it will default to the latest. You need to use install_prebuilt() to install one of the other package for example (TinyTeX-0 or TinyTeX) e.g tinytex:::install_prebuilt('TinyTeX')
You need the last version of tinytex from CRAN for this.
Regarding TeX Packages
The binaries comes with a pre-installed set of TeX packages. The list comes from our test suites so that R Markdown and other related product can compile with their default template.
For missing packages, tinytex will parse the log to find the missing package, and try to install them using tinytex::tlmgr_install(). It is not the R package that is doing the download of the missing packages. The R function is just a wrapper around the command line tlmgr.
If this is not working well for you, it may be cause by the CTAN repository mirror that you are using. This is not a TinyTeX feature or tinytex configuration. This is relatated to TeX Live. You can see the repository used with tlmgr repository list (Doc about the command: https://www.tug.org/texlive/doc/tlmgr.html#repository)
Maybe changing the url to a better mirror could help, but in theory the best should be chosen but tlmgr.
Also, as you are mentionning CI, sometimes finding and installing all missing packages can be time consuming and the runner can not like this time spent and may timeout. (it happened on Travis for example).
Know that you can install a version of TinyTex with more packages (called TinyTeX) by following one of the installation method in https://github.com/yihui/tinytex-releases
Know that with the R function you can also pass a vector of TeX package to install. If you have the list, this would be faster as it would not have to find the missing packages. We do that in our CI sometimes to speed things up.
If you can share more about the error you get and the issue you have (like error or log messages), we can look into this further.
Hope it helps