Hi,
I don't see why it would be different between products with and without variants.
I checked on my end and I don't find that version of the plugin:
www.regularlabs.com/extensions/componentsanywhere/changelog
The latest is still the 4.6.0
I actually tried to reproduce the problem and I do have it on my website regardless of whether the product has variants our not.
I do have the "Pass on Cookies" setting activated in the components anywhere plugin, but if I add such code at the beginning of the view file product / show.php (which displays the product details page) via the menu Display>Views:
<?php echo '<pre>';var_dump($_COOKIE);echo '</pre>'; ?>
It displays an empty array when I access the article page with the product:
monosnap.com/file/JihYm2tnrr9lvJmfemlRVujnHHe97W
But If I access the product page directly, I do see the Joomla cookies:
monosnap.com/file/ndRRJhHACx3cYqMjxPQOHjOD4yr7Lu
And some of these are used to maintain the user session.
Without the cookies, it's normal that the selected currency is lost in the area loaded by components anywhere.
Supposing that you have the 4.6.1 of the plugin on your end, you can do that test yourself. That way, you can confirm whether the cookies are there or missing.