Thank you so much. I appreciate your detailed suggestions!No. I haven't used the projector lights, but LEDs draw considerable less current then the equivalent factory fitted incandescent globes, therefore there is less drain on the battery.
The puddle lights should switch off as soon as the front doors close, you can check this by opening the driver’s door & operating the door switch to see if they switch off as soon as you press the door switch. Do the same with the passenger front door. That will prove the door switch operation. If the interior lights are timing out after the user pre-set time when the doors close (the default should be 30 seconds but it can be reduced) then the doors are operating the door switches correctly & the BCM is dimming & switching the interior lights off correctly (you may not see LEDs dim though).
Jump starting a battery won’t charge a battery up (well it will a bit but hardly at all), it will only supply current to allow the modules to control the start sequence & to supply the starter motor with enough current to turn the engine over & therefore start the car. After jump starting, the battery will need to be charged, either by driving the car a considerable distance or by charging it with a quality smart charger like a CTEK. Did you do this?
I would suggest monitoring the battery voltage with a voltmeter (if you don’t own one a reasonably cheap digital multimeter will do the job). Leave the bonnet unlatched & measure the voltage at night & again in the morning. See my earlier posted voltage graphs in this topic to get an idea how slow the battery voltage falls overnight. When you say “it was fine until about two weeks ago when it went dead”, how much was the Outback driven prior to this? Enough to keep the battery in a good state of charge?
You probably know this, but make sure the cargo hatch is closed, that can discharge a battery overnight if left open. Make sure the interior lights are off but with LEDs fitted that isn’t as much of a problem. But using the infotainment unit without the car running takes a considerable amount of current.
You can monitor the volts via the Factory Setting screen on the infotainment unit (which is good when you are driving), but when the vehicle isn't being driven it requires opening/closing the driver’s door. A voltmeter is better, or if you want to go the extra mile I can highly recommend a battery monitor similar to what I have posted about in earlier posts.