The synapse server was connecting and registering all 35 of its tools, but
no profile listed it under tools.*.mcp, so build_tool_list never handed a
single one to an agent — the hub was up and unreachable at the same time.

server_admin takes read + write (32 tools: events, deliveries, rules,
sources, targets, routing); secretary takes read only (15). The admin group
— key_issue, key_revoke, settings_put — is deliberately left out of both:
issuing and revoking hub keys stays a manual operation.