What the everloving fuck
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Put a 12V to 24V inverter just inside the firewall. This will isolate the "noisy" vehicle power system from the more fragile solar panel and power bank. It won't be nearly as expensive as an inverter that can survive the engine bay.
The 24V output of the inverter should be wired in parallel with one or several 24V solar panels, then into the power bank input. In this configuration the vehicle power system and solar system can charge the power bank simultaneously. No action is needed to change between power modes. However, you should have a main cutoff switch, disconnecting all power from the power bank.
I highly recommend a Victron brand inverter.
Warning: Direct current (DC) systems present an extreme fire danger. Every wire must be the correct gauge, every fuse the right size, every crimp correct. No piece of the puzzle is difficult. But, one must have all of them to build a safe and reliable system.
Yes, you'd damage the car's electrical system. First of all it's not designed to feed in energy through that outlet. It's made to output energy.
And most importantly: 24V is way too much. 2 times the intended voltage would fry most electronics. Your stereo, the power steering, airbags, ... There is a good margin and car electronics are designed to be pretty robust, but you're pushing it.
I think they're still fine because what happens is your car battery absorbs that extra voltage. But it's really dangerous. On a sunny day you'll charge your car battery beyond the 14V or so the chemistry can handle. And at that point it'll degrade fast. The acid in there is going to start to boil, producing hydrogen, so in addition to a destroyed battery, you're in for a small explosion if you're very unlucky. And once the battery is gone it'll start frying the cars electronics because now there isn't anything keeping the voltage down.
Get a switch that exclusively connects either the car or the solar panel to the bluetti. One switch that switches between two things, not an On/Off switch. And make sure it's rated for the current.
Edit: Or a relais that toggles between both. It can switch if there's power on the 12V rail, and connect the bluetti to either or.