Kind of a few good reasons, tactically, security, and mechanically/battery, why these dont exist already....
I would recommend something simpler- a Gun Vault, the kind that has a hand print on it to line up your fingers by feel. It has some knockout holes to bolt/chain it into the car. Uses a battery but can also be connected fairly easily into the electrical DC system. And u locks in a couple seconds.
Short of that, modify one of the police style locks like Santa Cruz and carry an AR pistol... Typically powered when car is on, with a wired button release.
I was told that Blac Rack systems can also be used to secure a pistol, have never used them, but from what I can see they are primarily for long guns. They squeeze together so I guess maybe a pistol could just clamp inside it? Not something I would do but just throwing it out there to look into.
Nobody makes something like you are describing. But one that could be activated by a button switch would be very easy to make from something like a Gun Vault setup, just rip out all the electronics and hard wire to a powered switch instead.
Personally, I want something that I can unlock when the key is not in the ignition. Pain in the neck to have to get a key out when grabbing a rifle out of a police vehicle rack, (while you already have a pistol available), so I can’t imagine screwing around trying to do that to get your only available weapon...
Just my two cents, I used various police racks for decades and have used several different pistol systems in my personal vehicles.
Also- you want it secure in some manner when driving. A couple lb pistol can go flying in a crash and clobber someone in the head. I have seen crashes where similar items caused pretty serious injuries. A loaded pistol isn’t something I want flying around...