For that, you should be able to go by the previously-known battery specs. If the battery was marked as capable of 1600w, then assuming that's continuous it would be 1600w / 48v would be 33A, so the BMS would need to be limited to a 33A shutdown to protect the cells the same as the old one. (it can be and should be capable of more, so it doesn't blow up under spikes of load, but it should be limited to shutdown at that limit, after maybe a few seconds of higher than that).
If you can tell how many parallel cells are actually in the pack then if we go by the current listed on the specs I saw, you would multiply that p number by that current (7.5A), to get the max current the cells should handle. They don't specify if that 7.5A is continuous or peak; so you'd have to either test or assume.... Testing means putting a continuous load on the cells equal to the number of p cells x the current you want to test them at, and monitoring temperature and voltage drop vs no load. If temperature goes up rapidly or voltage drop is severe then that 7.5A should be used as a peak rating, if temperature rises only slowly or voltage drop is minimal, it is probably continuous.
Since it's marked as 13Ah, then if they are 2.5Ah cells, that gives 5.2p, which doesn't work. So it must either be 6p, and they are derating the Ah, or more likely it is 5p and they are exaggerating the Ah (because we all know no company would ever do that

).
If it's 5p, then 5 x 7.5A is 37.5A. If it's 6p then 6 x 7.5A is 45A. My guess is that the 7.5A is really a peak rating (regardless of how it's advertised).
The 48v, if used the way most packs are specified, means it needs to be a 13s BMS, not 14s, since those cells are marked as 3.7v (nominal; they'd be 4.2v full). 48v / 13s = 3.7v.