Integrate Agents Core Web into the Core monorepo

[sam2tom]

Summary

• integrate Agents Core Web and the reusable TypeScript Agents API client into the Core monorepo
• add workspace, Makefile, CI, Core Doctor, Playwright, documentation, and screenshot integration
• preserve the latest Core runtime, MCP, executor, and Subagent changes from main
• keep import-only provenance snapshots out of the recurring Web development gate

Validation

• make check-web
• TypeScript typecheck
• Core Doctor: 63/63
• Agents client: 228/228
• Web: 571/571
• Playwright: 73/73
• production build
• Claude adapter: 120 passed, 4 platform skips
• MiniMax companion harness: 6 passed, 1 platform skip
• git diff --check

make check passes sqlc, Go, database, Core API, Claude, Web, Playwright, and companion harness checks on macOS, then reaches the unchanged Rust executor and fails on Linux-only O_PATH / st_dev behavior. Linux CI runs the complete platform gate.

The agents-api / sessions check currently reproduces the same pre-existing Expected BadRequestError failure as main run 35650179913. This PR does not change the failing Core service, contract, daemon, or internal paths.

No real model or paid provider call was made during validation.

Scope

This PR integrates the Web project into the Core monorepo. It does not deploy services or remove the source repository, branch, or worktree.