There are a few options for getting the running/live config via API, and it depends exactly what you want, there is nuance between the options, and based on this thread so far I'm not sure which is most appropriate, so I will share them all and let you decide which one meets your requirements:
https://{{host}}/api/?key={{key}}&type=config&action=show
https://{{host}}/api/?key={{key}}&type=op&cmd=<show><config><running></running></config></show>&target={{managed-device-serial}}
https://{{host}}/api/?key={{key}}&type=export&category=configuration
Saving the running config as a named "snapshot" can be done with:
https://{{host}}/api/?key={{key}}&type=op&cmd=<save><config><to>{{config-snapshot-name}}</to></config></save>
Hope that helps!
Help the community: "Like" helpful comments, and click "Accept as Solution" if you found your answer 🙂