Issue #3568942 by cicciobat: Add form context to distinguish Search API Page block and page forms

Francesco Maria Battagliarequested to merge
issue/search_api_page-3568942:3568942-add-form-context into 8.x-1.x

Also fix the missing dependency injection for FormBuilder, see #3568963

Closes #3568942

Edited by Francesco Maria Battaglia

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