My view is that if you are starting to learn R, you should begin only with tidyverse.
I have been using R for some years, and today regularly perform various kinds of analyses. Everything is so simple with tidyverse - why make it harder for people to get started? I recall one concrete example in last few months when I had to google a base R alternative.
To tidyverse, add in the RStudio cheat sheets, and you can immediately do 80-90%+ of what you need.
As an instructor, you can talk about base R along with the idea of packages - it is not a complicated concept to explain. But move on to the practical stuff, quickly.
Of course you'll be using <-, c, %in% etc... but these are details. For the stuff you need to actually do, start with tidyverse verbs.
I pity people who I run into who are learning R and their instructors/courses teach them base verbs - tidyverse was invented to make common tasks simpler. The syntax is close to perfect (I would argue), it is readable, it is fast - and it is a joy to use.
If you are teaching/learning R to get stuff done, why not minimize the time to getting useful results?