To troubleshoot why this button text is not available in the Content Template translation or the String Translation, I'll need to see how WPML and this template are configured in the admin area.
Can you please share temporary admin login details, in reply to this message?
Note: Your next reply will be private and making a complete backup copy is recommended before sharing the access details.
While I can see the issue with the read more button's text not getting translated on your website, I couldn't reproduce this on a test website. This suggests that something specific to your website is involved.
To troubleshoot this, I'll suggest the following steps:
1. Please make sure that WordPress, active theme, and plugins are all updated to the latest versions.
2. It would be interesting to test this with all non-Toolset and non-WPML plugins disabled and a default theme like Twenty Twenty-One.
If it's fixed, you can start adding the disabled items, one by one, to narrow down to a possible conflicting one.
3. In case the issue still persists, I'll need your permission to download a clone/snapshot of the website to investigate this on a different server.
I hope this helps and please let me know how it goes.
I've been having some inconsistent results between your website's clone and my clean test website, which suggests that it might be something server related.
Would it be possible for you to share the admin access details of the staging website again?