feat: add AI platform push integration admin toggle

[walker-tx]

Stack context

This PR is the third part of a four-PR stack that moves organization product-feature management from the legacy Dashboard Platform Admin surface into the standalone Admin application.

PR #6036 establishes the shared product-feature API and isolated Admin contract, and #6000 generates the private same-origin Admin SDK from it. This PR applies those foundations to the Admin Features page: it uses the generated contract for exhaustive feature classification and closes the remaining parity gap by adding AI Platform Push Integrations. The final PR can then remove the superseded Dashboard feature-management route.

What this PR does

• migrates Admin feature reads and mutations onto the private generated Admin client
• classifies the generated feature contract exhaustively so new features require an explicit UI decision
• adds AI Platform Push Integrations to the organization Features page
• preserves cache updates, rollback behavior, unauthorized redirects, pending state, and canonical organization lookup

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