Demystifying the Usage of that

Hi,

In the question "The much debated position on the relationship between the GDP and the industrial revolution claims that the acceleration of the GDP that begun 300 years ago with the advent of the industrial revolution, and continued since then." suppose one encounters two option as below

A.that began 300 years ago with the advent of the industrial revolution and has

B. began 300 years ago with the advent of the industrial revolution and has

Which one of the two will be correct?

As per some explanation "The acceleration of GDP" will not be having any verb if "that" is present in the sentence as "That" will take both verbs "began" and "has continued" Option B is correct

Now since "that" is referring to noun phrase "acceleration of GDP " then why Option A, as given above may not be correct?

In many cases of Relative Pronoun modifier clauses "that" becomes the subject referring to the preceding noun entity and fulfils the SV Pair condition ,then why in those questions the "noun entity" and "that" is not viewed separately as seen in the above question?

Example: Retailers do not approve of the apps that allow shoppers to perform immediate price-comparison by scanning a product on the shelf.

In this sentence “that” refers to the preceding noun – apps - and the entire underlined clause modifies this noun – apps.
As you can see, “that” is the subject of the purple clause. Its verb is “allow”.

Then why the below statement cannot be correct?

The much debated position on the relationship between the GDP and the industrial revolution claims that the acceleration of the GDP that began 300 years ago with the advent of the industrial revolution and has continued since then

Please explain the above query?

Also if possible one module on "Demystifying the Usage of that" may be included in the course

Regards