feat: add support for system picker in setDisplayMediaRequestHandler (#43680)

* tmp

Co-authored-by: Samuel Attard <marshallofsound@electronjs.org>

* feat: add support for system picker in setDisplayMediaRequestHandler

Co-authored-by: Samuel Attard <marshallofsound@electronjs.org>

* oops

Co-authored-by: Samuel Attard <marshallofsound@electronjs.org>

* Apply suggestions from code review

Co-authored-by: Erick Zhao <erick@hotmail.ca>

Co-authored-by: Samuel Attard <sam@electronjs.org>

* stuff

Co-authored-by: Samuel Attard <marshallofsound@electronjs.org>

* well...

Co-authored-by: Samuel Attard <marshallofsound@electronjs.org>

* seems legit

Co-authored-by: Samuel Attard <marshallofsound@electronjs.org>

* chore: update patch to handle screenCapturer

Co-authored-by: Keeley Hammond <khammond@slack-corp.com>

* feat: modify API to use useSystemPicker

Co-authored-by: Keeley Hammond <khammond@slack-corp.com>

* fix: gate ScreenCaptureKitPicker to macos 15 or higher

Co-authored-by: Keeley Hammond <khammond@slack-corp.com>

* fix: don't use native picker with legacy media selection

Co-authored-by: Keeley Hammond <khammond@slack-corp.com>

* chore: code review, boolean set & docs update

Co-authored-by: Keeley Hammond <khammond@slack-corp.com>

* fix: add cancelCallback

Co-authored-by: Keeley Hammond <khammond@slack-corp.com>

* docs: clarify session & desktopCapturer docs

Co-authored-by: Keeley Hammond <khammond@slack-corp.com>

* chore: update patches

---------

Co-authored-by: trop[bot] <37223003+trop[bot]@users.noreply.github.com>
Co-authored-by: Samuel Attard <marshallofsound@electronjs.org>
Co-authored-by: Samuel Attard <sam@electronjs.org>
Co-authored-by: Keeley Hammond <khammond@slack-corp.com>

shell/browser/api/electron_api_session.cc

@@ -1607,7 +1607,7 @@ void Session::FillObjectTemplate(v8::Isolate* isolate,
                  &Session::SetPermissionRequestHandler)
       .SetMethod("setPermissionCheckHandler",
                  &Session::SetPermissionCheckHandler)
-      .SetMethod("setDisplayMediaRequestHandler",
+      .SetMethod("_setDisplayMediaRequestHandler",
                  &Session::SetDisplayMediaRequestHandler)
       .SetMethod("setDevicePermissionHandler",
                  &Session::SetDevicePermissionHandler)