You dont need that big a facility to store it in text form. If you could collect the data, you could store the text every word spoken by every person in the US for,the past two decades with a unique number to ID the speaker and a timestamp of when the word was spoken, all uncompressed, on an obsolete hard drives stored in your closet.
The technology to store all U.S. conversations on a hard drive I am not familiar with. That’s a question I could ask my Microsoft relative. However, the Utah NSA stores world wide data, including photos and videos from you cell phones and emails. That’s why we have intelligence satellites.