[sitecore-embedded-jss-app] Remove usage of SitecoreContextFactory

[sc-illiakovalenko]

Remove usage of SitecoreContextFactory

Description

Motivation

How Has This Been Tested?

Types of changes

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to change)
• Documentation update (non-breaking change; modified files are limited to the /docs directory)

Checklist:

• I have read the Contributing guide.
• My code follows the code style of this project.
• My code/comments/docs fully adhere to the Code of Conduct.
• My change is a code change and it requires an update to the documentation.
• My change is a documentation change and it requires an update to the navigation.