Can I manually order task context groups?

Yes, in task dashboard views and other grouped views. Open the layer icon on the right-hand side, set group order to Manual, then drag the groups into the order you want.

You cannot manually order the built-in task groups on the daily note. Those sections are fixed. See Can I fully customize the built-in task sections on daily notes?.

For more on arranging groups in views, see Group By.

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