This feature request already exists, and it’s almost exactly what you’re describing, an override for the Anthropic base URL: Request to override Anthropic Base URL
It’s better not to create a duplicate, but to collect votes in one place. Drop a like there and subscribe, and you can also add your Azure AI Foundry use case in the comments. The more specific the scenarios are, the clearer the priority is for the team.
Also keep an eye on Allow use of Claude models through Azure Foundry, it’s specifically about Claude via Foundry.
I can’t share an ETA for either, but both are being tracked.