Hello,
We have confirmed from the Test Site, the Add to Cart on Mobile is working fine with Cart showing after add to cart correctly. Here is the Test Site URL where you can check for yourself too: https://blackpearlspro.com/woodmart_support/shop/
So, on your Site can you please once make sure your WoodMart theme and Core plugin is updated to the latest version and then check back the issue again on your Site. The latest version of the Theme running is 7.0.4 and the Core version running is 1.0.35. If it is not updated then you can update the Theme and Core following the Documentation Guide: https://xtemos.com/docs-topic/update-the-theme/
If the issue still persists after updating the Theme and Core plugin, then could you please once try deactivating all the third party Plugins on your Site remaining the Theme required ones activated. If the issue gets resolved, then reactivate them one by one to see which Plugin is causing the issue.
If somehow issue still persists, then please take complete Backup of your Site first, then provide us the WP-ADMIN Login details of your Site in the Private Content field along with the permission to completely debug your Site which includes deactivating all the third party Plugins and removal of on-Site Customization changes too, so that we can thoroughly check this issue on your Site and assist you accordingly.
Best Regards
.
