Explicitly declare the dependencies

[quangIO]

By default, npm hoist undeclared dependencies to node_modules. However, this behavior doesn't apply to pnpm. This allows building with pnpm without shamefully-hoist.

[pavelfeldman]

• We don't use pnpm and it is not covered in the tests, so it will regress.
• Different versions of playwright and playwright-core in deps is a recipe for disaster!