...when someone sends me a signature request via Sign
You're not seeing the uploaded image or smart phone image signatures that you’ve saved because the person who requested the signature from you has restricted the types of signatures they accept.
Your requester would need to change his/her settings to accept uploaded signatures or smartphone signatures.
For info on how the sender can turn this setting on or off, please see "Restrict signature types."
...on the mobile app
The mobile app and the web app do not currently sync together, so you will not see any of your saved signatures from your website account on your mobile app account. Please note that you can’t save signatures on our mobile app.
...when using an embedded flow (Embedded Signing, Embedded Requesting)
When using any embedded flow, Sign does not expose saved signatures. This is because with these flows, Sign does not authenticate the user—the app owner does. Since the app owner authenticates the user, Sign wants to protect sensitive data (such as signatures) from being exposed.