At my wit’s end with site performance issues for large WooCommerce website

your site is not working now.

It’s up for me. and we have no monitor down alerts. It may be slow as I described above. Are you getting an error?

you may restricted some ips.

Can you share your IP or country?

even the google crawler cannot reach.

What is your IP or country?

Turkey

Please try again.

Cache is working successfully. as far as I see that you are using Nginx web-server. If you are using a server-side cache system, you should disable it.

Thank you. I cannot see your attachment.

Is there a way to properly speed up WooCommerce category queries such as https://collectorstudio.com/product-category/literature-manuals-brochures-etc/brochures-manuals-tools-etc/

yes, there is.

See https://www.wpfastestcache.com/tutorial/woocommerce-settings/, particulary disabling cache clearing after orders change. This could be triggering unnecessary purges of your popular categories.

Your popular category pages will be re-cached very quickly after purging them, while others won’t if they have not been visited. That’s normal if you don’t preload your cache.

If you do preload, the site will gradually be cached in the same order every time, so you’ll see quicker caching of he categories that are cached first when the cache is cleared.