subscriber: make format::Writer::new() public (#2680)

## Motivation

As seen here #2512 and #2223. Previously pr'ed here #2525, but no progress has
been made there for quite some. I have applied the suggested changes. Not sure
the formatting of the doc is sufficient or otherwise correct

## Solution

Make the `format::Writer::new()` function public. I don't see any obvious
trade-offs, but I am not familiar with the larger direction of
tracing/subscriber, so I may be wrong.

Closes  #2512
Closes #2223

Co-authored-by: Cephas Storm <[email protected]>
Co-authored-by: Eliza Weisman <[email protected]>

tracing-subscriber/src/fmt/format/mod.rs

@@ -418,7 +418,19 @@ impl<'writer> Writer<'writer> {
     // We may not want to do that if we choose to expose specialized
     // constructors instead (e.g. `from_string` that stores whether the string
     // is empty...?)
-    pub(crate) fn new(writer: &'writer mut impl fmt::Write) -> Self {
+    //(@kaifastromai) I suppose having dedicated constructors may have certain benefits
+    // but I am not privy to the larger direction of tracing/subscriber.
+    /// Create a new [`Writer`] from any type that implements [`fmt::Write`].
+    ///
+    /// The returned `Writer` value may be passed as an argument to methods
+    /// such as [`Format::format_event`]. Since constructing a `Writer`
+    /// mutably borrows the underlying [`fmt::Write`] instance, that value may
+    /// be accessed again once the `Writer` is dropped. For example, if the
+    /// value implementing [`fmt::Write`] is a [`String`], it will contain
+    /// the formatted output of [`Format::format_event`], which may then be
+    /// used for other purposes.
+    #[must_use]
+    pub fn new(writer: &'writer mut impl fmt::Write) -> Self {
         Self {
             writer: writer as &mut dyn fmt::Write,
             is_ansi: false,