Despite the common misconception that NID is the heritage:operator inscribing historical monuments, in fact each regional heritage protection officer (wojewódzki konserwator zabytków) acts independently in their designated area. NID is merely responsible for gathering and propagating data about the heritage. These refs are therefore likely to have been reused in different regions. Besides, over decades the scheme that the inscription refs follow has clearly been changing, not to mention different regions were likely never guaranteed to follow a uniform standard. The regions themselves also changed along with reforms to the country’s administrative divisions. So that’s why these refs are not unique and don’t give you a feeling of order and consistency.
For looking up inscription refs the PDFs you linked seem to be the best bet. They are regularly updated and include a nr rej. for every entry. Why zabytek.pl doesn’t display the most commonly used ref is a mystery.
The piece of wall you’re showing us was added long ago and it might be hard to find out where the mapper took the number 629125 from. The objects is also a tad misplaced and has the lower side wrong. Given the ref doesn’t appear anywhere, I can’t find any other proof that it is a protected monument (other perhaps than the inscription of the entire spatial layout of Jarosław’s old town) and finally that the mapper slapped the name of the nearby city gate onto this object, I’d go ahead and remove the heritage tags.