Right-clicking on the Drafts icon in the Dock shows a similar menu to the Menu Bar, where you can either create a new draft in the main window or use the simpler quick-capture window to save (or open) the draft. Since I launch Drafts automatically at login, it will always be active so it appears in the Dock, but you might choose to eliminate the redundant Menu Bar option.

Currently, I assign the Drafts app to All Desktops, so that it appears in every one of my macOS desktop spaces. You can choose This Desktop to only assign it to your main space (Arc browser and Obsidian, for me); in that case, macOS will automatically switch over to your main space whenever you launch a new Draft. With my setting, the draft will be created in the current space and avoid extra space switching.