The vehicle is on for high power use like a winch or more powerful air compressor.
The modern high power connector for electronics is USB-C, but the LC is only 15W and probably just 12V. The Bluetti and others are multi-voltage and high watt capable (either 65W or 100W).
The point of the hybrid is not to leave it on for long term low wattage usage, but to always have a source to easily recharge a power station or the starter battery. If I'm remebering correctly the LC does have a low voltage shutoff for the 12V system when the vehicle has the ignition in ACC.
So the choice is between adding a conventional battery in parallel with the existing starter battery or purchasing one of two small power stations. I think most people will find small power stations more useful. Not only do they provide high power USB-C but can be moved around camp.
The upside of a traditional house battery could be powering fixed vehicle mounted camp lights. Although traditionally one reason to have vehicle mounted camp lights was to access the energy in the vehicle battery systems.
We don't yet know winch requirements, but I find it unlikely that Toyota didn't design a 12V system that could not run a front winch. A high end ARB tire inflator uses about 800W which the vehicle can easily support with the engine in the on position.
Unlike conventional vehicles we completely avoid needing special alternator additions, portable generators or solar to keep up with higher power needs in camp. The reason solar is so often now paired with power stations is that the 12V/120-300w energy typically available in vehicles is not enough to recharge batteries in a reasonable time.
This is my impression for the accessory power wattage, correct me if I am wrong:
Cooler: 30-60W on 120V AC/DC
Laptop: 60-140W on USB-C
Offroad Light: 50-400W on 12DC direct wiring
Stereo: Not sure but I’ll say the same level or less of the offroad lighting, 12V direct wiring
Winch: 50- 200A on 12DC direct wiring so 600-2400W for a less than 10000lbs winch
For cooler, laptop there is no doubt 12V starter battery or power station should handle it.
For offroad light bar and stereo shorter term 12V battery should be fine, but long term the starter battery will need some support, this is where the power station or backup battery could help
For winch I am not sure. Ideally if traction battery can handle it would be great. But DC-DC conversion from 288V to 12V at thousands of watt is very taxing, loads of heat will be generated. This is also the area the stock alternator can’t catch up the discharge rate. For EV like Tesla Cyberatruvk or F-150 EV it wouldn’t really be an issue. But LC is not designed to be operated by hybrid battery, that is why I said until we fully understand the capability and control logic of the traction battery I will leave it untouched
In addition, one thing I worried about my Bluetti is that the cabin temperature during summer is very hot. Even if it is safe enough not to catch fire, the battery life might get some real impact. So there is going to be high wear to keep the power station I side the car during summer if we don’t do other thing to help.