Obsidian

Obsidian puts a markdown editor over a folder of files on your disk and adds the things a folder cannot do on its own: links between notes that work in both directions, a graph of those links, a canvas for arranging ideas spatially, and a plugin library deep enough that most people's setups look nothing alike. There is no account, no sign-up and no feature held back. The free version is the whole app.

The reason it belongs on a site about not renting software is the vault. Your notes are .md files in directories you picked, readable in any text editor, and they stay there when you stop using Obsidian. That makes the switching cost close to zero, which is not true of any hosted tool it replaces.

Two things to be clear about. The app is free but not open source, so this is a gift from a company rather than a guarantee, and the $50-a-year commercial licence is optional support — Obsidian's own licence page says the app is free for commercial use. Sync is where the money actually is: $4 a month billed annually, with no lifetime option. iCloud Drive, Dropbox or a git repo do the same job for nothing, and the mobile apps are free either way.

If you want something that organises itself, this will feel like homework. Obsidian rewards people who enjoy building their own system.