My name is Rae and I work for Shopify. Thanks for reaching out about this, and welcome to the Shopify Community.
This login issue may be tied to the browser you’re using, or to the cache on your browser. To check if this is the case, open Weglot through your Shopify admin using a Chrome browser and try to log into your account from this window. Please also ensure that the cache on Chrome has been cleared by following these steps.
If you are still having the same issues after trying this on Chrome, I recommend reaching out to the Weglot developers about this directly. Weglot is a third party app, so their developers have the best knowledge to help troubleshoot this further. Their contact information can be found here on the ‘Support’ section on the right hand side of the page. They also offer support directly through their website here.
This information should get you on the right track, but let me know if you have any other questions or concerns!