Hi Jorrig,
I don't know if there is anyone who has combined live videoconferencing with other experimental elements like mouse tracking. In theory, I think this is possible given the existence of sites like Omegle that create interactive video chats in a browser. I don't see any in principle reason why this couldn't be combined with an experiment on the same page. But, this would definitely be hard and require a substantial amount of development work.
One critical factor here is whether you need to synchronize the video conferencing with other experimental events. If you only require a very loose synchronization, then one option would be to use standard video conferencing software like Zoom for the communication and implement the experiment in existing experiment software, like jsPsych. You could have these two windows open in parallel. If you need participants to interact with each other outside the video call, like seeing each other's mouse movements, then there are some platforms that are developed for group-interaction studies, including oTree, Empirica, and NodeGame.
Cheers,
Josh