Add support for Tweedie and Poisson regression for multi-output tasks

[nickcorona]

Description:
Currently, XGBoost supports Tweedie and Poisson regression for single-output problems. However, there is no direct implementation or support for multi-output tasks for these objectives. Adding support for these regression types in multi-output settings would allow users to model complex datasets where multiple targets need to be predicted simultaneously.

Motivation:

• Multi-output regression is increasingly relevant for real-world applications (e.g., demand forecasting, insurance claims, energy consumption, etc.).
• Tweedie and Poisson objectives are widely used for their suitability in cases involving non-negative data, zero-inflated distributions, or mixed discrete-continuous outcomes.
• Extending these objectives to multi-output regression will make XGBoost more versatile and competitive.

Proposed Solution:

• Extend the implementation of the tweedie and poisson objectives to handle multi-output regression tasks.
• Ensure compatibility with existing XGBoost features like early stopping, evaluation metrics, and prediction interfaces.
• Additional Context:
• Multi-output regression is supported for objectives like reg:squarederror and reg:linear, so adding Tweedie and Poisson support should align with existing multi-output functionality.

Environment:

• XGBoost Version: x.x.x
• Python Version: x.x
• System Information: (Optional, add system details if needed)

[trivialfis]

Thank you for raising the issue.

Yes, it's our goal to support all objectives for multi-output. At the moment, it's a priority issue instead of a technical issue. Progress is being tracked at #9043 .

I will close this issue to focus the discussion in the linked thread.