There is no simple answer. There is a compromise, and depending on which factors are most important in each case, or for each user, my recomendation would be different. In addition, personal preference, is a valid reason for choosing among those computer languages or "ecosystems" that are good enough for the job. We are most productive if we feel confortable and enjoy the work we do, so it matters a lot that the tools we use feel good to us. However, one important point is that Tidyverse and data.table are built on top of R, which means that one needs a good understanding of R for debugging problems with either of them. So, starting by properly learning R is worthwhile the effort.
For someone doing data analysis for a living, updates and deprecations maybe tolerable because it is easier to keep up to date with the changes. For the occasional user like many researchers in acatemia or part-time maintainers of R packages, such changes can be a pain. I very much appreciate stabilty and backwards compatibility (I love TeX and LaTeX) but still use the Tidyverse for some data analysis scripts, but rarely pure "Tidyverse". I used data.table for a while some years back, but for the rather small data sets I work with, it did not feel worth the effort of learning it in depth.
On the other hand, trying data.table and learning to use the Tidyverse, even if nowadays I use it rather selectively, has taught me new ways of solving problems and of thinking about data analysis. So, spending time with the three "ecosystems" was time well spent. One thing that I learnt by using R for the last 25 years is that many of the apparent performance bottlenecks in R can be avoided within R itself if one knows how. Performance of R has also improved over the years.
What I wrote above is just my opinion at this time. It is based in how I use these ecosystems. Without actual planning it, my routine has become to use base R unless there is a clear advantage in using the Tidyverse packages and functions. I do not currently use data table, but I would at least try it again if I had to improve performance for large data sets. @Chr I disagree with you about casual users, but mainly because of the constant evolution of the Tidyverse. R is mostly in the 90's but the design is no longer in flux. Again a compromise. @Spacedman I agree with you, I think. These "ecosystems" are tools. Any tool needs to match the task, but also fit the user of the tool.