Sourcegraph Notebooks PM here. We have a notepad feature you can enable that basically does what you're describing and allows you to create a notebook from the saved content in one click. There's a button to enable the notepad on the notebooks page (https://sourcegraph.com/notebooks or https://<your-sg-url.com>/notebooks).
It follows you around as you navigate search results and files and you can add searches, files, and file ranges to it, as well as notes for each item. Quick demo video: https://storage.googleapis.com/sourcegraph-assets/docs/image...