The shop and category images, as well as gallery images, are still using the default WordPress image URLs instead of being replaced by the R2 URLs, resulting in broken image links on the pages. Is there a setting available to switch the URLs?

Are the images considered Media within WordPress? On the presentation side, if they are being presented by a third-party plugin or theme, it would need to make sure to use the standard WordPress hook for generating attachment URLs. It's the wp_get_attachment_url filter that does the backend processing for figuring out what the true URL is.

Themes/plugins should be using that normally (it's the standard way to do it in WordPress itself), if something isn't, you probably want to report it to the author because it's more or less a bug (or at least a severe oversight). Again, that filter isn't coming from us, it's the normal one that's supposed to be used for anything WordPress (including stock WordPress itself) since WordPress 2.1.

I am using the WoodMart theme (https://woodmart.xtemos.com/).

Probably makes the most sense to report it to them. Not about adding support for this plugin exactly, but for them to support the normal WordPress filter I linked to above. That’s the “proper” way for anything to handle image URLs.

when I use plugin like https://www.superspeedyplugins.com/product/external-images/
They change product image and gallery image to external url and that work well . also they provide some image options that work with most of the case.

Can I request a refund? I need to find an alternative solution.

Sure