I’d personally avoid implanting chinese chips of unknown quality and stick to the ones that Dangerous Things sells. Safety is very important when you’re putting things under your skin.
And saving up for a safe chip is cheaper than a nasty infection or heavy metal poisoning…
According to the screenshots that you posted, both the card and the fob are Mifare classic 1K chips so you’d be looking at the xM1 or flexM1 implants if you want to clone those as the NTAG216 chip can not emulate them. However, you might be able to convince whoever manages the access control system to try to enroll the NTAG chips but keep in mind that this might not work.
That’s not recomended; read this post on the subject: