Deprecated and moved writeflusher impl to internal pkg

[krissetto]

What I did

• Deprecated and moved writeflusher impl to internal pkg (since it was exported and a few external projects seem to use it)
• Added new internal writeflusher implementation, removing some old buggy bits and adjusting the Flush() func to also call WriteHeader() on the underlying io.Writer if it's an http.ResponseWriter.
  This is needed to ensure that we don't try to send headers multiple times if the writer has already been wrapped by OTEL instrumentation (which doesn't wrap the Flush() func. See Syslog entry: "superfluous response.WriteHeader call" in Docker 25.x #47448)

How I did it
I moved the old impl to internal/writeflusher, and created a NewLegacyWriteFlusher() func that the old exported NewWriteFlusher() func calls to maintain the original behavior. All code using this deprecated version from the ioutils pkg should be unaffected

How to verify it
Usual tests should run as usual, as this shouldn't have any effect

Description for the changelog

Create new internal implementation for writeflusher and deprecate the old one

A picture of a cute animal (not mandatory but encouraged)

[vvoland]

This is still used in a bunch of places in API, which makes the linter complain:

api/server/router/build/build_routes.go:234:12: SA1019: ioutils.NewWriteFlusher is deprecated: use the internal/writeflusher WriteFlusher instead. (staticcheck)
	output := ioutils.NewWriteFlusher(ww)
...

we should also replace these with the new implementation.

[vvoland]

Do we need to add the deprecation and removal notice to https://github.com/docker/cli/blob/master/docs/deprecated.md? @thaJeztah

While not strictly an API, if we're bothering with the deprecation-cycle anyway, perhaps it wouldn't hurt to call it out in our docs.

[krissetto]

This PR was created as a solution to the "superfluous call to writeheader" issue. It seemed like a good moment to go ahead and deprecate the old writeflusher implementation which was exposing some known buggy functionality (

moby/pkg/ioutils/writeflusher.go

Lines 54 to 64 in ae976b9

	func (wf *WriteFlusher) Flushed() bool {
	// BUG(stevvooe): Remove this method. Its use is inherently racy. Seems to
	// be used to detect whether or a response code has been issued or not.
	// Another hook should be used instead.
	var flushed bool
	select {
	case <-wf.flushed:
	flushed = true
	default:
	}
	return flushed

)

If we merge #47796, this PR will no longer be necessary unless we still want to deprecate the old writeflusher implementation