Important: the closest alternatives are personal, the rest are team tools
Vikunja is the closest self-hosted match, with projects, lists, Kanban, Gantt, recurring tasks, subtasks, labels, and apps for web, desktop, and mobile. Super Productivity is a local-first personal planner, and Donetick covers shared chores. Plane, Huly, OpenProject, Taiga, Operately, and Macro are team project-management platforms, which is more than a personal to-do list needs.
Recurring tasks and natural language
Vikunja and Donetick support recurring tasks, and Donetick adds natural-language input and fair assignment for shared chores. Super Productivity adds time tracking, Pomodoro sessions, and issue-tracker integration.
License details
Super Productivity is MIT, OpenProject is GPL-3.0, Taiga is MPL-2.0, Freeter is GPL-3.0, and Vikunja, Plane, Donetick, and Macro are AGPL-3.0. Huly is EPL-2.0. Operately's repository is Apache-2.0 except its ee directory, which is under an Enterprise Edition license. Check each repository's current license before adopting.
Local-first vs self-hosted servers
Super Productivity and Freeter store data locally and need no server. Vikunja, Plane, Huly, OpenProject, Taiga, Donetick, Operately, and Macro run as servers you host, which adds team access and sync but requires maintenance.