1- It is not this version of Brook that will defeat a TR. Current Brook is stronger than its WCI version and will still receive a great power-up to do so.
2- We do not know the conditions that Perosperos arrested them. Perosperos managed to arrest the entire vinsmokes family in an instant when they were off guard. Peros may have caught them off guard when they fought with the randons.
3- The fruit of Peros is quite hax. Caesar also knocked Luffy out with hax, this does not necessarily explain the level of power.
4- Brook and Chopper were already exhausted fighting other opponents
5- Katakuri was there, so he may have interfered
2- We do not know the conditions that Perosperos arrested them. Perosperos managed to arrest the entire vinsmokes family in an instant when they were off guard. Peros may have caught them off guard when they fought with the randons.
3- The fruit of Peros is quite hax. Caesar also knocked Luffy out with hax, this does not necessarily explain the level of power.
4- Brook and Chopper were already exhausted fighting other opponents
5- Katakuri was there, so he may have interfered
Katakuri never interfered, he knew that Perospero could easily take on Brook and Chopper with no problem.
Here is Katakuri sitting in chapter 876.
And here is still sitting in chapter 877 the same chapter that we see Brook and Chopper being restrained by Perospero.
Brook and Chopper are both strong yes, but Perospero was just on a whole different level. Some people have even said that Perospero might even be commander level and that he might also be stronger than Snack, so despite being a veteran he might actually be even above that but I personally don't think he's commander level.