Hope you are doing well and sorry for the trouble. As described the screen turns to grey when you try to add new signature to the PDF.
Would you mind sharing the version of the Adobe Acrobat/ Reader DC you are using? To check the version go to Help > About Acrobat and make sure you have the latest version 21.01.20135 installed. Go to Help > Check for updates.
Also, please check if you are able to access the Save As Dialog. Open a PDF > Go to File > Save As.
As a quick workaround you can login to https://documentcloud.adobe.com/ and go to Fill and Sign and create new Signature/Initial. Once done, come back to Acrobat and launch Fill and Sign app on a PDF and wait for some time. The newly created signature/initial should get synced to your application.