As a self hosted I only know Kanboard but it only do kanban afaik.
Otherwise I'm using " todoist " (obvious name). It's a web app, with android app also. It provides several points of your list but not all:
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Several board/lists (called "project").
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Can share any of the projects with someone else.
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Task + subtask with due date and priority (and even assign to someone).
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Keep history
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Add tags or comment to tasks and subtasks
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Several options for notifications
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Reminder/alaram, but only for paid version (never tried ...)
I don't think there are options for repeting tasks (maybe with the paid version). And no integration with home assistant provided.