[WIP] Rewrite zombienet-polkadot-functional-0012-spam-statement-distribution-requests

[AndreiEres]

Fixes #5973
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[paritytech-workflow-stopper]

All GitHub workflows were cancelled due to failure one of the required jobs.
Failed workflow url: https://github.com/paritytech/polkadot-sdk/actions/runs/13457625070
Failed job name: cargo-clippy