fix: align backend with protocol interop contract

[alpha912]

Summary

• accept application/ld+json for LOOP writes and map duplicate writes to 409
• enforce strict federation handshake schemas and add parity automation
• sync backend schema copies with the updated protocol definitions and expand tests

Validation

• bun test
• bun run typecheck
• bash scripts/check-protocol-parity.sh

Note

• This PR is easiest to merge after the loop-protocol branch because the new parity check compares against the protocol repo default branch.