Hi Qing,
Thanks for the prompt reply. What I'm seeing is slightly different to your screenshot, but still similar.
When going to Settings > Library Settings and then selecting the column, I see:

It is using a closed term set, and so Fill-in choices have been automatically disabled. There is no default value. Under List Content Type, it is possible to see that the column is set to optional:

We did indeed test the same document library (our site only has one document library) with the new and classic experience. The issue only occurs in the new experience. As shown in the screenshot below, when uploading a document to the library, it is not
marked as a required field and I am allowed to leave it blank.

However, after selecting a value in the 'Client' field and saving it, I receive the error message shown in the screenshot of my original post stating "You must specify a value for this required field."