I selfhost Vikunja on a small 1GB RAM VM. It has views for list, table, Gantt and Kanban (I assume that's what you mean by not manually reordering?) You can setup reminders for your tasks like any project management tool as well.
You can access its web interface via port 3456, so no syncing or external app is needed, it's all browser based. Of course, you can setup a wireguard VPN to access it anywhere.