There’s currently no way to view QM data in the Site Editor itself (for a few reasons, including the fact that it’s mostly an SPA, the admin toolbar is hidden, and most performance concerns happen in its REST API requests). That might change in the future but it’s definitely not a priority for me.
What QM does fully support is showing debugging info when you view pages that you’ve built with the site editor.
If you’re moving into modern WP (FSE etc) you may want to be aware of some issues that the Site Editor in particular has and how Query Monitor might help surface these:
My original Woo ticket re: exceeding host’s “program executions”: github.com/woocommerce/woocommerce/issues/60795
(they did not believe me at first, and then once they saw the problem, Woo limited the number of requests but it still is too high on a site with more than one template. I even disabled Heartbeat API at the host’s suggestion. But Woo is still causing way too many requests/program executions [10x Siteground’s limit, which is a highly rated host!].
Someone else noted this issue and was also brushed aside by engineer as it being a low priority issue: github.com/woocommerce/woocommerce/issues/60393
Gutenberg team noted similar issue with the Gallery block as well and addressed it: github.com/WordPress/gutenberg/issues/10994
Controls were added in Gutenberg to disable the preview entirely because of related issues of so many requests in the Site Editor: github.com/WordPress/gutenberg/pull/71972
Pressable (by Automattic) even noted similar issues and workarounds: pressable.com/knowledgebase/understanding-and-troubleshooting-admin-ajax-php-in-wordpress/
You may also be interested in how the plugin NOTED! handled this. Similar to QM it appears in the wp-admin toolbar up top, but inside Gutenberg it is under the three-dot dropdown on upper right since the top toolbar disappears
https://wordpress.org/plugins/noted/
