Hi there, I'm Matt Sergei (do call me Matt, please) and can help you with R and Google Cloud -
what seems to be the problem? You can receive the JSON file from Google and use it to authenticate in practically any programming language (and Google SDK for it e.g. javascript/Node.js, PHP, Python etc).
So having an R/Shiny script to authenticate can be done using the same principles.
I can setup a test script (I have used Shiny server on Mac in the past - will need to set it up again since I don't have Linux server handy) and will need your credentials to authenticate, script this with R and test.
Otherwise I'm a webmaster and developer for 26 years, using R for years even before my currenrly on hold PhD studies where I was the only to demand using R instead of SPSS for all statistics related work :-).
Regards and hope you're safe,
Matt