After some troubleshooting, I found a solution that worked out which is to Include Windows 10 LTSB in WSUS Products. To do that,
- Open the WSUS Administration Console.
- Go to Options > Products and Classifications.
- Under the Products tab, scroll down and select Windows 10 LTSB.
- Click OK to save the changes.
By doing this, your WSUS server will be able to recognize and manage updates for Windows 10 under the long-term servicing agreement, including the 2021 LTSC version.
I realized this when I searched for the latest updates for "Windows 10 version 21H2" on the Microsoft Update Catalog and noticed that the July updates appeared under the product Windows 10 LTSB (see attached screenshot).
Hope this helps anyone facing a similar issue!