What’s the best way to build a cross-platform open-source planner app?

Godot is still a reasonable option, especially since you already know it. For a productivity app, though, you may need to build or find UI components for text editing, accessibility, window layouts, and platform conventions that are more common in application frameworks. If you’re comfortable with it and the interface isn’t extremely complex, using Godot could let you move faster than learning an entirely new stack.

Think about synchronization before committing to the user interface. If people are expected to use the same data on multiple devices, you’ll need a storage and conflict-resolution strategy, usually involving a server or a user-controlled sync service. A browser-first design can establish that foundation, after which you can create native clients for the platforms that matter most.

A web application is probably the most practical starting point. Build the core planner in the browser, then package it for desktop and mobile if needed. That gives you broad platform coverage and makes synchronization between devices easier. Frameworks such as Flutter or React Native are other options if you want a more native-feeling interface, but they still require learning their ecosystems.

Start with a much smaller scope: choose one platform and one planning feature, such as a cross-device to-do list. Once the data model, editing flow, and storage are working, expand into mind maps and additional clients. Trying to solve desktop, mobile, synchronization, and several kinds of planning at the same time will make the project difficult to test and maintain.