feat: enable queue up new tasks

[OscarLigthart]

Context

This PR implements the ability to queue up new tasks. In a recent PR, #59764, this functionality was added to core. In this PR, the call is added to the API, and the button is enabled once more.

Example

After running we see:

With the old ones not having another task try:

Related Issues

• closes: Queue up new task button is always disabled in UI #57051

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Generated-by: Claude Opus 4.6 following the guidelines

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