This is not a technical question.

The immediate pro-market position is that if third-party clients are allowed / possible, Anthropic should be allowed to favor its own clients with lower prices.

But the position can go further if the service in question can be considered infrastructure. For example, a company that owns a mobile network may be required to let virtual operators use their infrastructure for a reasonable price. And a company owning a power grid may be required to become a neutral infrastructure provider that is not allowed to generate/sell power.

EDIT: Anthropic should not be allowed to favor its own clients with lower prices.

Anthropic is neither a monopoly nor has a dominant market position. Generally standards applied to companies like that are very different due to good reason.