Align capability key to SEP-2133 extensions format

[jeongukjae]

Both SDKs now use Capabilities.Extensions with key "io.modelcontextprotocol/interceptors". Previously C# used the short key "interceptors" and Go used Capabilities.Experimental. SEP capability example updated to match.

https://modelcontextprotocol.io/seps/2133-extensions

[jeongukjae]

@PederHP there was some misalignment on initialization. I think I found all references in csharp sdk, but might miss others. please have a look.

[PederHP]

LGTM

[PederHP]

The capability key rename looks complete — every key site now uses io.modelcontextprotocol/interceptors (C# all routes through InterceptorProtocolConstants.ExtensionCapabilityKey for both read and write; Go server.go uses extensionID; the docs/sep.md example matches). The remaining bare "interceptors" literals are JsonPropertyName/json tags on the list-result payload, not the capability key, so those are correctly untouched. 👍

Two doc spots were missed by the accompanying Capabilities.Experimental → Capabilities.Extensions surface move, though — they still describe the old surface and now contradict the code:

• go/sdk/doc/DESIGN.md:53 — "injects interceptor metadata into Capabilities.Experimental["io.modelcontextprotocol/interceptors"]" → should be Capabilities.Extensions[…] (the key string itself is already correct; only the surface is stale).
• go/sdk/doc/CONFORMANCE.md:27 — "Interceptor metadata injected into initialize response via Capabilities.Experimental" → should be Capabilities.Extensions.

(csharp/sdk/docs/ARCHITECTURE_PHASES.md:49 mentions Experimental too, but that's the transparent proxy generically mirroring all capability surfaces — not the interceptor key — so it's fine to leave.)

— Posted by Claude Code (Opus 4.8) on @PederHP's machine; this review comment was written by Claude, not Peder.

[jeongukjae]

@PederHP Thanks! I addressed those docs

[PederHP]

LGTM