fix: add type checks for TypeScript workspaces

[abhinavkr26104]

Closes #1446

Summary

• add check-types scripts to the web app, browser extension, and memory graph playground
• add check-types scripts to the UI, hooks, lib, and validation packages
• reuse the browser extension’s existing compile command for type checking

Notes

The docs workspaces remain excluded because they do not contain a TypeScript configuration or TypeScript source to check.

Validation

• confirmed Turbo now resolves executable check-types commands for all affected TypeScript workspaces
• ran bun run check-types

The expanded check currently exposes pre-existing type errors in @repo/ui/other/anonymous-auth.tsx. This is the intended coverage change; those errors were previously skipped and should be fixed separately before requiring the expanded command to pass in CI.

[ved015]

LGTM !