Update setprecision docstring and add NEWS entry for thread-safe behavior

NEWS.md

@@ -15,6 +15,7 @@ Language changes
 is considered a bug fix ([#47102])
 
   - The `hash` algorithm and its values have changed. Most `hash` specializations will remain correct and require no action. Types that reimplement the core hashing logic independently, such as some third-party string packages do, may require a migration to the new algorithm. ([#57509])
+  - `setprecision` now utilizes `ScopedValue`, enhancing thread safety when setting precision levels. This change allows for safer precision adjustments in multi-threaded environments. ([#51362])
 
 Compiler/Runtime improvements
 -----------------------------

base/mpfr.jl

@@ -1054,11 +1054,15 @@ Set the precision (in bits, by default) to be used for `T` arithmetic.
 If `base` is specified, then the precision is the minimum required to give
 at least `precision` digits in the given `base`.
 
-!!! warning
-
-    This function is not thread-safe. It will affect code running on all threads, but
-    its behavior is undefined if called concurrently with computations that use the
-    setting.
+!!! note
+    Temporarily sets the precision for BigFloat operations to `precision` bits within the
+    scope of function `f`. This function is now thread-safe due to the use of `ScopedValue`,
+    ensuring that precision settings do not interfere across threads.
+
+Example:
+    setprecision(256) do
+        # Operations here use 256-bit precision
+    end
 
 !!! compat "Julia 1.8"
     The `base` keyword requires at least Julia 1.8.