Trying to automate a 3-way light circuit with no neutral

I am trying to figure out a way automate a 3-way lighting circuit with no neutral wire in either switch box. I've been told it's been wire as a "California 3-way".

The light circuit consists of 5 LED cans and one (switched) outlet that powers a neon sign. What is the easiest way to automate this? The lights will usually be controlled by the wall switches, but I sometimes want them to be controlled by an automation.

I use Home Assistant so I need something that is compatible with that.