As far as a toggle option is concerned, that all depends on how integrated you want it to be with BI itself.
Reading between the lines a bit it seems you want to know about the current BI camera status inside HA. If that were done then you could create an automation that runs the appropriate enable/disable script.
However, so far i have not found a way to always confidently know the actual camera status from HA’s point of view. Inside BI, per camera, there is the ‘Watchdog’ tab that allow for monitoring if the camera loses connection. On loss of connection or restoration of connection you can run some alert, like publishing a custom MQTT topic. This topic can then be monitored by HA via an MQTT switch or MQTT trigger to take some action. This is what i do today for my two “sometimes powered on” wifi cameras.
Unfortunately the Watchdog feature in BI does not seem to detect if a camera is Disabled. It only seems to work if the camera is not sending any signal (powered off). Currently i dont know any way to retrieve the status of enabled or disabled.
So, what options do you have? In HA you could create an input_boolean for each camera you want to work with. Then modify those scripts to turn the boolean on or off depending on which script you run. Problem is that the boolean would not be syncronised with the actual BI camera status. Hence the ‘confidently’ comment from earlier.
Since you are using the HACS BI integration, maybe the developer of that solution has some additional ideas.
As for your second question about displaying BI cameras directly in Lovelace, other than the way it’s being done now. I have some thoughts but no final solution. The issue i have found so far is that if i simply embed the bi ui3 url somewhere in view or card then, the site does not load. Even if using ui3 anonymous connection. I have been thinking about this topic myself & have not yet settled on a final solution but here are a couple of ideas to get you started.
Create a new view & on the settings tab enable ‘Panel Mode’.
Add Webpage card to that new view.
For you card you could add the all cameras index stream using this url. http://yourserver:port/mjpg/index
This option works for me. However, its just the index stream & you can’t drill to a specific camera like this. It’s not ideal & probably not something i will use, other than for testing.
Add a button card to any view like this image.
When you click that button the BI UI3 page will load.