Setup `tsc --watch` workflow in examples and CLI project templates

[bajtos]

When I was working on the extension starter project, I added configuration allowing developers to avoid possibly long compilation time by leveraging tsc --watch mode. See DEVELOPING.md for the documentation.

We should apply this configuration to everything that can be used independently from our monorepo:

• All example packages
• CLI templates for app and extension projects

This is a follow-up task for #836.

Acceptance criteria

Update the following places in our monorepo

• Example packages (replace this checkbox with an up-to-date list of example packages)
• Extension project template
• Application project template

For each place, make the following changes:

• Setup build:watch and test:dev scripts in package.json (source)
• Add .vscode configuration with "Watch and compile TypeScript" and "Test and lint" tasks - (source)
• Add DEVELOPING.md file describing dev setup and workflow for developers using VS Code but also for developers using their own IDE/editor (source)

[shimks]

@bajtos This feels like a duplicate of #1259. Could you please confirm?

[bajtos]

Yes, this looks pretty much as a duplicate of #1259, which was implemented via #1336.