Hello Romuald,
yes, your suspicion is right, Fozzybear is a non-official NXP mascot ;-)
The PN531 is not activly supported anymore by NXP, and is not recommended for new designs. Therefore NXP will probably not change the document status of this product.
The USER MANUALS for the NFC devices Pn532 and PN533 describe the command sets and firmware of the NFC IC's, the DATASHEETS much more the hardware implementation and characteristics of the chips. Unfortunally it might still take some time until datasheets and other documents of the PN532 and PN533 will be available without password. The public release of the User Manuals is the attempt to fix the situation you mention, software development should be a little bit easier now.
I expect that the User Manual of the PN532 will be made public on the web soon. If there is an interest, I could post a notification.
Fozzybear