Send from Workbench
Sign is reachable from Workbench, so getting something signed does not mean leaving the chat you are working in. The connection runs both ways.
Start a request from a chat
Ask Workbench to send something for signature and say who has to sign it. What comes back is a signature request for you to check, with the send sheet holding what you asked for.
Nothing goes out from the chat. The request reaches the signers only when you send it yourself, in the same sheet described in Sending for signature, and the same rule applies: it will not send until every signer has a spot.
Asking for a signature request in chat prepares it. It does not send it. The send is always yours to make.
Take an agreement into Workbench
The other direction starts in the Sign register. The three-dot menu on any agreement row has Open in Workbench, which takes that agreement's documents into a Workbench chat, where you can work on them as you would any other document.
The agreement stays where it is in Sign while you do. It keeps its stage, its matter, and its place in the register.