Ash here from the Shopify team.
Thank you so much for including the links in your post. I was able to follow the first link and replicate the issue you're experiencing. This definitely seem odd, and I'm happy to help get to the bottom of this. In order to determine what's wrong here, I'll need to start by getting some additional information from you. Could you please reply to this post and let me know the following:
Once I have that additional information I'll have a better idea of what's going on, and how we can move forward to resolve this.
Thank you for the additional information! While it's still possible this is app-related, it's less likely if you haven't installed any new applications recently.
Let's determine if this is related to the theme you're using. In order to do so, head over to your Online Store> Themes, and scroll down to the area where you can "Explore free themes". Install any free theme on your store, and then preview your site in that theme (you don't have to publish the theme, the option to preview the theme will be in the Actions menu). Once previewing your site in an un-edited, free theme, visit an affected product page and see if the variant selector works as expected to update the price of the variants being selected.
Please reply back here to let me know the results of that test.
Thank you for testing that and letting me know the results. Since everything worked as expected in a free, un-edited theme, that tells me that the issue is within the Empire theme. Since the Empire theme is a third-party theme, our theme support team wouldn't be able to dig into the themes code to find the root of the issue.
Have you heard back from Empire's customer support at this time? For third-party themes, the best way to get support is through the original developer of the theme. If you're unable to get assistance directly from them, then I would suggest contacting a Shopify Expert for further assistance. Shopify Experts are trusted, third-party agencies and freelancers, who are available for hire by Shopify Merchants. You can visit their site here to contact an Expert, or post a job request and receive quotes from eligible Experts. This would be the next best alternative to getting assistance directly from the developers of Empire.