React wrapper: Enable TypeScript strict mode & ensure proper strong typing everywhere

[NOtherDev]

Context

How has this been tested?

Types of changes

• Bug fix (non-breaking change which fixes an issue)
• New feature or improvement (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to not work as expected)
• Additional language file or change to the existing one (translations)

Related issue(s):

1. RFC proposal: [RFC] Improving React Developer Experience #10767
2. Annotate Events functions types with this: Core as they are always bound #10812

Affected project(s):

• handsontable
• @handsontable/angular
• @handsontable/react
• @handsontable/vue
• @handsontable/vue3

Checklist:

• I have reviewed the guidelines about Contributing to Handsontable and I confirm that my code follows the code style of this project.
• I have signed the Contributor License Agreement
• My change requires a change to the documentation.