I beg to differ. Mathilde's experience with dwarfs so far suggests strongly that when information like this is offered to responsible leadership, what happens is they set upon a careful and deliberate plan to rip the offending party to shreds, over centuries if necessary.
In the case of Dwarf Chaos Cultists she's likely of the opinion that they SHOULD be ripped to shreds and sees no problem with it. Likewise she already understands it shouldn't be shared to the public, any more than finding chaos cultists in Stirland should be something shared to the council in general.
Mathilde had seen a lot of mature, reasonable if understandably very grumpy dwarfs. And Kragg has been goddamned exemplary in how he conducted himself.
He dislikes modern cannon, but they're in use and he just grumbles about their unreliability.
He dislikes Umgi magic, but he has conducted himself with reasonable courtesy and restraint, handling Mathilde's deeds with sour looks but recognizing she remains a credit to the team.
He hates the Greenskins, so instead of running out there and pasting them with his hammer in fury, he prepares, and stockpiles a massive array of runic weaponry for the day when he might see them DELIVERED.
From every indication, what she expects out of Belegar and Kragg when she tells them about the Dawi Zharr is:
-Plan for an eventual campaign against the Dawi Zharr, which will include scouting, mapping, determining forward bases, and overall a timescale of maybe 4-5 centuries.
-Prepare runes to fuck up heretical dwarf sorceror slavers
-Tell her to keep it secret. As she didn't tell the COUNCIL they can expect a certain degree of sense they would not normally expect of Umgi.