How can I make hubitat push switches operate smartthings hub bulbs?

[Cobra]

Look at hubConnect.
This gives you the ability to pass switches back and forth between ST & HE

[RELEASE] HubConnect - Share Devices across Multiple Hubs (no longer SmartThings!)

Current Release: 1.6.4 - December 29, 2019 HubConnect 1.x End of Life Notice With version 2.0 about to be released, there will be no further updates to the 1.x codebase and all official support will end on 4-30-2020. HubConnect - A new and improved way to connect and share devices across multiple Hubitat and SmartThings hubs to a central Hubitat hub. HubConnect replaces HubLink/Link to Hub and supports true bi-directional device linkages no matter where the device is physically located; …

Andy