Use `inspect` module for better logger control

## 🧰 Task

re: [#general > Logs widget for displaying all output (not just logging) @ 💬](https://napari.zulipchat.com/#narrow/channel/212875-general/topic/Logs.20widget.20for.20displaying.20all.20output.20.28not.20just.20logging.29/near/561769040)

I'd need to learn more about this, so this is a future goal. But, I'm happy to look into it if I find time / others would find this useful.
