Why are multiple 学s okay in the sentence 我学英语学了4年了 In this sentence, I do not understand the purposes of each of the 2 instances of the character 学.

我学英语学了4年了。
I have been studying English for 4 years.


In my naive understanding I would personally translate the English to Chinese as follows:

我学了英语4年。


I think this might be related to my confusion about the phrase 学英语. Is this a noun that means "The Study of English" or is it a verb like "to study English"? I can see why you might add a second 学 if the former is true.
The interesting phenomenon in this example is the use of 了。。。了 to indicate an ongoing action. In cases where the ongoing verb takes an object (like 英语 in your sentence), the verb is repeated. If the object is understood, it doesn't need to be repeated. For example, if you've established with your interlocutor that you're studying English, you might say 我学了一年了 (I have studied for a year).

As an aside, your "naive translation" would be closer to "I studied (i.e., completed studying) English ...". If this is your intent, a more apt translation might be 我学了四年英语