Dispatch is not a chat it’s the office manager
It's entirely possible that everyone else knows this and I've just been an idiot for ages, but I recently discovered that asking Dispatch to do the tasks and having them run within Dispatch is the wrong way to use it. It's able to communicate with Co‑Work, show tasks that are currently running, find previous tasks, and chat.
You can tell it to give those tasks instructions, create new Co‑Work tasks that have access to all the available tools you have connected, and it will provide updates on how those tasks are running if you ask. It can generally manage your entire Co‑Work and chat installation.
Posting this for the idiots like me who thought dispatch was a simple siloed chat.