Devices joined know first and foremost about the Controller that did the Include. Devices have storage for addresses of other devices to send a message to... but ONLY if that gets configured. Wink, SmartThings and Hubitat don't. Vera might, I just don't know.
Therefore, the rule of thumb is.. the Primary controller knows the most about what's occurring on the network, unless there's something that goes out of it's way to configure it.
Your SmartThings v3 could be linked to Hubitat by either HubConnect, Link to Hub, or OtherHub.
I have read about a HomeSeer to Hubitat tool, I read it went through Beta and would come out with a price, as is normal in the Homeseer world. I have never read of a similar Vera project.
Associations are not going to be undone by adding in additional secondary controllers. @ericm wrote a tool for associations to Inovelli products. I have not kept up to date on any generalizations of that code.
Remember, your Hubitat Hub is streaming events constantly. That stream can be picked up by anything on your network. You can add MakerAPI to expose some or all Hubitat devices to control by another system. This is the basis of @dan.t Homebridge rework and the Homeseer product as well. It would not be hard for someone with Vera skills to build a "HubConnect Remote Client for Vera" tool, but I simply don't know of anyone trying.
