Lazygit patches are a great way to do this. You can interactively select lines from commits to “pull out” making them easy to form new commits with. Takes some getting used to, but it is the exact flow you are talking about.

https://github.com/jesseduffield/lazygit?tab=readme-ov-file#...

Oh you edited to say drag and drop. Lazygit is a TUI and patches are very much keyboard driven. Still worth thinking about? It’s free!