So those are multiclass readers, but I would bet your access control system is only searching for 125kHz cards, which is why the system is not recognizing an xNT.
DT does provide support to help users interface with HID systems (search the forums for HID). It’s just not a huge team and contactless card technology is a large, complicated, fluctuating landscape. Also, every user’s system is configured differently. Unfortunately, a lot of the onus is upon you to learn more about the architecture and figure out what questions to ask.
Check out this HID brochure to learn more about the specific system you’re using. The fact that all the labels you posted pictures of say “Format: H10304” is really useful. Try scanning the the card you want to clone with Taginfo to see if there is any useful information on the HF side. You may also want to get a diagnostic card to determine how the system is configured.