Hi,
Yes, the NFC Reader Library is big. That is because it supports all protocols and different operation modes, such as EMVCo, NFC Forum or ISO/IEC.
Within the package is a DoxyGen documentation of it. The overview gives a good idea of its architecture and structure.
If you look at some examples they use only a subset of the NFC Reader Library to fullfill the needs of this particular example.
Operating on register level is for sure the slimest version. But implementation a anti-collision with it is also not easy.
I don't want to push you towards the NXP NFC Reader Library. I only wanted to point it out that it might help. Maybe the HAL (Hardware Abstraction Layer) for the CLRC663 will help you already a great deal to ease the process of operating the controller. If you stack the ISO/IEC-15693 protocol layer on top you need only a couple of APIs for all you described.
Porting the nfclib is actually quite easy. You only need to abstract the phDriver layer. Which consists of an GPIO Input (IRQ), Timers and BAL (Bus Abstraction Layer, which is the hardware interface to your front-end; Like SPI).
On the question if there is no documentation for your use-case at register level; The answer is unfortunately simple: No
For that exact purpose the reader library was developed. To ease the process of tag operations and not having to bother with the registers. Usually in a commercial reader you have to take care of a lot more as only the simplest tag operation. You have to take care of your analog parameters, power management, complying with different certification institutions, etc...
Of course if you need help with anything feel free to ask
Best regards,
Alexander