Can you scan your work card with the taginfo app and post some screen shots. Hide the UID so we can’t see it if it makes you feel better.
Looking at the info you have given I’m pretty sure the NExT won’t work for this as it looks like one of the newer mifar 1k with “increased security” you may be able to use an xM1 OR flexM1 but won’t know for sure until we see tag info.
Edit: love the edit @Backpackingvet 