It takes a bit of direct research, and don't trust summaries from non-specialists such as myself. I am not a lawyer, not giving legal advice, and not affiliated with RStudio. I am not claiming this reply is an answer. I am just trying to point out the topics I think one would need to research to answer your question. Or at least things to look for in answers.
To orient the bit. I would suggest researching all of the systems and licenses separately. In particular
tidyverse each may or may not bring in different license issues.
R itself is licensed GPL2/3. So if one doesn't want GPL software then it doesn't matter what R packages you use as
R already brings in GPL2/3 rights and responsibilities.
The GPL2/3 license has conditions about what a GPL2/3 item can be distributed with. One of these stats that things that are distributed with, link to, or even built on APIs must themselves have a compatible license when distributed. The MIT license is considered compatible with GPL. So the
tidyverse likely isn't introducing many more obligations than just using
R, as the MIT license is considered fairly permissive. However it also isn't freeing parties from the GPL2/3 conditions.
The open-source distributions of
Shiny are under an AGPL v3 license. This license is significant in that it grants rights to downstream users even without code distribution. Roughly: using the code grants the same rights to the user as distributing the code would, including a right to the source code under an AGPL v3 compatible license. This license is very different than the GPL2/3 or MIT licenses, so requires its own study.