Moving and renewing our Curcy license and plug-in to a new domain

Helly Curcy & Support Team,
We bought the Curcy plug-in in 2021. Prior to launching our actual live website, we installed Curcy on our staging site at first to test out the plug-ins functions.
After our website went live in 2022, the domain the plug-in was attached to was never updated, which must be corrected.

Staging site: http://www.laksen-sporting.macadesign.dk
Live site: http://www.laksen-sporting.com

We now experience technical issues with the plug-in, so we must renew the license and update the plug-in, but I have difficulties doing so, and therefore i need your help.
Our license and plugin was bought and installed about two years, and was expired some time ago, so we have not updated it.

We have used the same license keys on our live website as the staging site, but the license has expired been expired since May 2022. Please help us with:
1. Moving the license from our old staging site at http://www.laksen-sporting.macadesign.dk to our live site at http://www.laksen-sporting.com.
2. Guide us on how we should update the Curcy plug-in correctly on our live website
*3. How we prevent to interfere and mess up the API’s data fields and configurations.

*I am worried about how we can succesfully update and renew the license and plug-in, as we have an API connected to our WooCommerce, where some of the data fields/keys in the API are directly related to the Curcy plug-in’s data fields/keys in the WC REST API.