there's a popular meme from someone who failed to realize that the wouldn't have hot water during a power outage; and the bidet specifically would be cold. "religious experience"
They have self contained water heaters, seat heaters, drying air heaters, and ozone based deodorizers. They pre-mist the bowl sides when your first sit down to help keep the bowl clean. It's a pretty magnificent device. It's 25% of the way through the 21'st century, and I may not have a flying car just yet, but at least I have a robot to care for my tushy.
Prior to installing bidet seats throughout the house, we had handheld bidets that were attached to the cold water line. It's really never immanentized a "religious experience" so far as I have noted, and while the heated one is certainly more pleasant, a cold water bidet seems to function pretty well for hundreds of millions of people around the world.
So far as I know, I've been an American for the ~50 decades I've been on this planet, and I'd say ~85% of the people I interact with on a day to day basis were born in America. I've observed that it is a common American trait to form strongly held views about things where one has no experience, and to defend those views fiercely. The Dude said it best.
Not exactly sure what you mean by "bidet seat" vs "handheld bidet" based on context, but mine goes under a regular seat (seat isn't replaced) with controls jutting out the side. I have also used what I'd call a handheld bidet during an extended water outage. It was a squeezy rubbery thing from Amazon, a bit like a cycling water bottle, and I'd fill it up with water from a jug or sink depending on where I was (was not "attached to the cold water line"), then it squirts out water from an angled plastic tip. I found I had to be a lot more efficient with that to get the job done on one fill, but it was certainly better than nothing.
Thinking on it more, maybe your handheld was like a pressure washer, totally separate from the toilet, and what I had in mind would be called "portable".
The ones I have used in the last few years all have a small instant warmer unit. Japanese homes don't always have access to hot water tank & even the shower space is serviced by a electronically activated gas heater.
Source: I live here in JP, and my parent company's main revenue stream is from gas heaters OEM, heating appliances and even bespoke plumbing & installations.
Whole-house battery backup is a modern marvel, too. (We have 80KWH of stored battery capacity and it shifts grid load to non-peak hours to save huge amounts of money.)
Here is an instalation video for a geberit aquaclean: https://youtu.be/1GU7SBIJc6A
Or you can use a bidet with cold water, but good luck using that in winter when the water comes out at 10C.
It's legitimately disgusting that bidets aren't common America. Such unsanity bathroom practices.