Similar setup here. 12.9 Pro, Logitech K380. Since you’re using the K380, I’m assuming you’re mostly at a desk/table. I’ve used a Pencil for 2+ years, until they enabled mouse support on iPadOS. Now I hardly ever touch the Pencil. I basically only use it when editing photos, which isn’t very often, and could use the mouse for that instead with some muscle retraining. I doubt I’ll be buying another Pencil. If my current one died, I’d probably throw it an a drawer and forget about.

Long story short, try any cheap $20 BT mouse you find. Maybe you have one in a drawer somewhere like I did. Better than a Pencil for navigation since it lets you do any swipe gesture you can do with your finger. e.g., access the Dock, Command Center, slider-over apps, etc.