American here. Thanks to woot regularly selling them, I have a bidet on each toilet in the house. I have a battery operated travel bidet, because now I'm hooked.
It has certainly led to.... "Interesting" responses from house guests. There's always TP in stock, so it's not required. Butt I'm never going back if I can help it.
Not true for any of the six bidets I have owned. the wand sits very far back in the spray is in the opposite direction of where the wand is and the wand itself retracts into a cover while spitting water to clean itself.
And I have never even had a fancy one with power or heated water. All these just run off the pressure in the pipe.
both my grandmothers used to preclean dishes with the same instrument before putting them in the dishwasher. It was attached to the kitchen sink of course. When I first saw one in a toilet in SEA I thought 'what? But grandma how?'. She told me that dishwasher salesmen recommended them, and I always wondered how they made the jump from Butt to Wedgewood.
I bought a Toto HW300-W "Portable Travel Washlet" off Amazon (https://www.amazon.com/dp/B008O1G4LQ) back in 2018 and it still runs like a champ. The text is all in Japanese, but easy enough to figure out (or Google Lens it if you really want to know).
* Edit: I should note that I paid about half of the current list price :-O