Oda has consistently depicted Yamato as a formidable fighter (going so far as to essentially use Luffy as a hypetool for her), while Brook was never treated in that way.
I don't think Brook is analogous to her at all (for this any many other reasons).
It was still enough to make it clear that he was above Pica.
I agree with this. But there's no meaning saying Yamato > King if she demonstrates the ability to clad her attacks in Haoshoku, or deflects a Thunder Bagua, or any other such displays that make it clear she's very powerful.
King hasn't been suggested to be closer to Kaido than other subordinates are to their Captains. He's the de facto Vice Captain, but he hasn't even been portrayed as being superlative to Queen the way Kata was to Smoothie.
Sure, the Beast Pirates don't think Yamato is as strong as a Calamity. The Beast Pirates were wrong.
Yamato oneshot Ulti:
Sasaki was terrified when she bared her fangs at him:
Sasaki was shocked when she oneshot a Number:
It seems clear that the Beast Pirates simply greatly underestimated Yamato.
It may have also been the case that the explosive cuffs Yamato wore were laced with karouseki. Considering that there were also explosive karouseki cuffs in Udon and that Yamato is a Devil Fruit user, I think those cuffs were probably laced with karouseki.
So the Tobi Roppo were sent to apprehend a Yamato that:
- Could not use her Devil Fruit
- Was substantially weakened on top
And despite that, Yamato was still considerably stronger than expected (as evidenced by her performance vs Ulti).