Hello @SaltClick,
How are you creating the envelope for your experience cloud users?
If it’s through the DocuSign Apps Launcher, there is a method to Create a Salesforce Experience Cloud Envelope Template. To control if a new tab or window is opened depends on how the URL button behavior is configured. However, I just tested something similar to this and even though I have my behavior set to “Display in existing windows without sidebar or header”, it still creates a new tab. At the end of signing it returns back to the source record, but you would have two tabs now instead of one.
If you’re attempting to embed a URL from a Web Form or PowerForm, it looks like there’s an HTML Editor component you can use to create an iFrame. Similar article from Salesforce Trailblazer Community.