Dogfooding the new ESLint config in our repos with JS and TypeScript

[web-padawan]

Description

Let's adopt the new ESLint config in the following projects:

Top priorities

• [x] https://github.com/vaadin/web-components
• [x] https://github.com/vaadin/docs (latest branch)

Other projects

• [ ] https://github.com/vaadin/docs (hilla branch)
• [ ] https://github.com/vaadin/start (private repo)
• [x] https://github.com/vaadin/hilla
• [ ] https://github.com/vaadin/flow-components

[web-padawan]

Updated @vaadin/testing-helpers to use eslint-config-vaadin 1.0.0-alpha.10 with new TypeScript presets.

[web-padawan]

PRs for updating web-components and docs repo latest branch:

• https://github.com/vaadin/web-components/pull/5434
• https://github.com/vaadin/docs/pull/2090