What you need
Elementor 3.9 or newer, WooCommerce 8.0 or newer, and a published filter set. The widget file is read only after Elementor has loaded, so a site without Elementor, or with one that is too old, never meets it.
How it registers
On Elementor’s elementor/widgets/register hook. That is the hook Elementor 4 uses, because the older registration hook was removed there. If registering the widget ever fails, the plugin records that and tells the people who can fix it, on the screens that are theirs.
What it draws
The set, exactly as the shortcode would. We compared the HTML of the block, the shortcode and the widget for the same set on a real WordPress with Elementor 4.3 active, and it was the same. The widget has one control, the set to draw. Everything about the filters stays in the set, so editing a set changes it everywhere it is placed.
Where it draws
On the shop page and on product category, tag and brand pages, like every other way of placing a set. On any other page it draws nothing for visitors.
What we have not tested
We have not been able to try the widget inside an Elementor Pro Archive Products template, because that needs a paid Elementor Pro licence we do not have. The script knows that widget’s container, and it should work. Try it on a staging copy first, and the Archive Products guide says what to look for.