Prevent duplicate Quick Edit save requests - #12869

This is a solid, minimal fix for the actual root cause of #25696: a shared saving guard set synchronously before the request is sent means a second click (or Enter keypress) while a save is in flight returns false immediately instead of firing a second request that can later operate on a row the first response already replaced/removed. It also matches the approach afercia proposed for this exact ticket over a decade ago ("when saving maybe it should just return false").

I checked out the branch, ran a full rebuild, and ran the QUnit suite plus typecheck:js — all pass, including the two new tests. CI's own Coding Standards/PHPUnit-equivalent checks are green too; the one red job (PHP 8.0 / MariaDB 12.1) is an unrelated infra failure (composer update couldn't reach packagist.org), not something this diff caused. .always() correctly clears the flag on both success and error/network-failure paths, so there's no way to get the button stuck.

One thing worth a mention on the ticket rather than blocking here: saving is shared per editor instance, not per-row, so opening Quick Edit on a different row while another row's save is still in flight will silently no-op that click with zero feedback until the first request resolves — same "should we show a busy cursor" concern azaozz raised in comment 16 back in 2015, still open. Given requests are typically sub-second this is low-impact, but it's the kind of thing that's easy to miss testing manually since it only shows up under real latency.

Small nit: the file's top-level namespace docblock documents @property {string} type / @property {string} what for inlineEditPost — worth adding @property {boolean} saving there too for consistency, alongside the inline comment on the property itself.