The first alternative's advantages are hard to ignore. As for the lone disadvantage, here are questions related to increasing long or heavily indented notebook (dropdown) title visibility:
Would it be possible to add a mobile tooltip (like Search has) to the notebook (dropdown) title in the toolbar? Edge case notebook names could then show inside the tooltip, wrapped to fit the viewport width.
Would it be possible to extend the notebook dropdown menu to the right viewport edge (mostly for portrait mode)? Yes, the menu edge and caret won't align. However, on-screen context and the beta feature of tapping the dropdown field to clear the dropdown should suffice.
I think there's room to add icons to the toolbar, especially if the above is possible. Other mobile editors tend to have 2-6 commonly used icon buttons on the right side, as seen in these examples: 7 of the Best Markdown Editors for Android and iPhone - Make Tech Easier
This is off-topic, but how about adding other common actions to the toolbar when appropriate? For example, I'd find the ability to sync or check when Joplin is syncing without leaving the sidebar open helpful. I'd also find the ability to pin a few hamburger menu options to the toolbar helpful for quicker action access when viewing or editing a note.
Edit: To make the above on topic, pinning specific plugins to the toolbar could also be as helpful as pinning extensions to a desktop browser toolbar.