Fixes https://github.com/zed-industries/zed/issues/12054

Replaces the `copypasta`/`smithay-clipboard` implementation with a new,
custom one

TODO list:

- [x] Cleanup code
- [x] Remove `smithay-clipboard`
- [x] Add more mime types to the supported list

Release Notes:

- Fixed drag and drop on Gnome
- Fixed clipboard paste on Hyprland