Thanks for your patience.
When creating the API url, please make sure that the privacy mode is set to "individual-related". Otherwise SoSci Survey prevents mapping of SERIALs and the address entry.
Then, when downloading the data, n Download Data please select the Variables tab, and check the option "Download mailing address entries".
In your download there will then be a variable PS_UID (one of the last variables) that contains the UID that you have specified when creating the URL.
Please be aware that you are handling person-related data according to GDPR in that case, and you will need an extended DPA, see https://s2survey.net/DSGVO/