apacheGH-41420: [R] Update NEWS.md for 16.1.0 (apache#41422)

### Rationale for this change

Update NEWS.md

### What changes are included in this PR?

News updates

### Are these changes tested?

No

### Are there any user-facing changes?

No
* GitHub Issue: apache#41420

Authored-by: Nic Crane <[email protected]>
Signed-off-by: Nic Crane <[email protected]>

r/NEWS.md

@@ -20,10 +20,26 @@
 # arrow 16.1.0
 
 # arrow 15.0.2
+* R functions that users write that use functions that Arrow supports in dataset queries now can be used in queries too. Previously, only functions that used arithmetic operators worked. For example, `time_hours <- function(mins) mins / 60` worked, but `time_hours_rounded <- function(mins) round(mins / 60)` did not; now both work. These are automatic translations rather than true user-defined functions (UDFs); for UDFs, see `register_scalar_function()`. (#41223)
+* `summarize()` supports more complex expressions, and correctly handles cases where column names are reused in expressions. 
+* The `na_matches` argument to the `dplyr::*_join()` functions is now supported. This argument controls whether `NA` values are considered equal when joining. (#41358)
 
-# arrow 15.0.1
+# arrow 16.1.0
+
+## New features
+
+* Streams can now be written to socket connections (#38897)
+* The Arrow R package now can be built with older versions of the Arrow C++ library (back to 13.0.0) (#39738)
 
-# arrow 15.0.0
+## Minor improvements and fixes
+
+* Dataset and table output printing now truncates schemas longer than 20 items long (#38916)
+* Fixed pointer conversion to Python for latest reticulate to ensure data can be passed between Arrow and PyArrow (#39969) 
+* Check on macOS if we are using GNU libtool is and ensure we use macOS libtool instead (#40259)
+* Fix an error where creating a bundled tarball with all dependencies was failing on Windows (@hutch3232, #40232)
+
+
+# arrow 15.0.1
 
 ##  New features