feat: merged data_studio__list_connections tool + AGENTS.md TS style alignment (0.1.3) - #19

Summary

Implement the merged data_studio__list_connections tool (epic #9) — lets AI agents discover all database connections across both backends before calling tools — and align the codebase with the AGENTS.md TypeScript style guidelines.

Changes

Feature: data_studio__list_connections

• src/connections.ts (new): listConnections() — fetches connections from all backends in parallel, tags each with its backend, skips unreachable backends
• src/backends.ts: listTools() now returns { tools, connections } — previously discarded the connections field from bridge responses
• src/index.ts: synthesizes data_studio__list_connections — injected into tools/list and handled in CallTool before the routing table
• Tests: +3 (tests/connections.test.ts) — merge across backends, skip unreachable, empty result

Style: AGENTS.md alignment

• function declarations -> const fn = (...) => ... (10 occurrences across src + tests)
• interface -> type where type suffices (9 definitions)
• Zero class / for loops / in-place mutation in the package

Release

• Version 0.1.2 -> 0.1.3, lockfile regenerated from clean state (npm ci verified)

Why

Before this, agents had no way to discover available connections via MCP — they had to guess connection names from tool descriptions. With this tool, the agent flow is: list_connections -> pick connection_id -> call database tools.

Companion PR: geek-fun/sqlkit#128 (sqlkit bridge now returns real connections instead of []).

Verification

• 18/18 tests pass
• tsc --noEmit + lint:check clean
• npm ci verified on regenerated lockfile