Brunilda didn't come back after tracing the trail of the assassination attempt to its origins. Instead, she enlightened him through the messaging mechanic before announcing she was heading back out to scope out Basilea City.
As Basilea City was a sprawling area by the sea, its buildings much more spread out than Mecane—which tended to build efficiently and upwards—there was a lot more ground for the feline to cover.
There was also the message that had to be passed to Jack Vengulls safely. Mattheus wrote a letter before stuffing it in the cat's pouch through the System. It would be bizarre for the merchant to pull out a pristine letter from such a small pouch but Mattheus figured Jack already associated this specific business partner with the weird and improbable.
Meanwhile, Mattheus just mentally waved her to go on, preoccupied with the identity of someone who tried to kill him.
Someone he didn't think he'd even met since arriving here.