Improve the quality of the NEWS file

The RStan NEWS file is often out-of-date (see https://github.com/stan-dev/rstan/issues/746) and even though it's now up to date (in terms of the actual date) the contents leave a lot to be desired. For example:

Tue July 7 2020
1. Bug fixes (presumably incomplete)
  * Better handling of NAs in monitor() and functions it calls
2. Features (presumably incomplete)
  * The sbc() function now has a save_progress argument thanks to jpritikin
  * The code compilation now uses the Curiously Recurring Template Pattern
    (CRTP) thanks to wds15

Especially since there are no other RStan release notes, it should be a priority to keep the NEWS file up to date.
It's pretty easy to keep it up to date if bug fixes and new features are done by opening issues and PRs. This is good practice and what we do for all of our other software (all other R packages plus the non-R interfaces too), so it should really be done for RStan too.

Start by reviewing the RStan NEWS file and the outdated-release discussion in issue #746. Compare the current entries with the bug fixes and features described in this issue, then determine how the file should be maintained; done means the NEWS file is current and substantially more informative than the example shown.