Fix lint tooling and move publishing to Node 22

[rcosta358]

Closes #124.

Update ESLint, remove obsolete test scripts and unused tooling, and move publishing to Node 22. Fix existing semicolon violations.

Validated on Node 22: dependency install, lint, type checking, production build, and extension installation.

Generated by Codex.

[CatarinaGamboa]

One small thing for #124's Node 22 move, outside this diff:

.devcontainer/devcontainer.json still uses mcr.microsoft.com/devcontainers/javascript-node:20. The point of the move is that the Vitest and @vscode/test-electron versions added later in this stack need Node 22, so anyone working in the devcontainer will hit that once #140 / #144 land, while CI on 22 passes. Suggest bumping the image to javascript-node:22, and optionally adding "engines": { "node": ">=22" } to client/package.json.

Reviewed with Claude Code (reviewer + adversarial agents per PR, findings checked against the code before posting).

[rcosta358]

Updated the devcontainer to Node 22 and added Node >=22 to the client manifest and lockfile in 6120840. Lint and extension packaging/install passed.