What is the idle check ceremony?

Not sure. I normally drive the car in ECO but recently haven't been regularly in ECO mode. I will pay attention to the mode next time. Thanks.

 

When ECO is on, it allows the engine to shutoff earlier in the warmup. I can't remember the exact number but 140F or so versus 160F without ECO on.

 

Pearl S starts to allow shut-off at around 40C coolant temp when in "ECO". Pearl (GII) didn't allow engine shut-off until coolant was up around 60C (the first time, after the first time the shut-off temp dropped to around 55C). Relating to when the A/C system is calling for heat. At start-up she will shut-off based on cat temp if the A/C is turned off. That can take from 10-60 sec. If the car was warm and re-started she will shut off almost right away, and sometimes will not even start the engine.

The O2 sensor before the cat(s) is used mostly for mixture control, the O2 sensor after the cat(s) is used mostly for exhaust gas temperature measurement. Don't want to melt the cat! I say "mostly" because they are used for much more. Modern "pollution control" systems are very evolved, work quite well, and do much more than they did when they acquired the name "pollution control system".

If you noticed the (s) I put in there it's because these days there are usually more than one catalytic converter. This is in response to the requirement of control during warmup, which was excused in the past. So a smaller cat will warm up and start working much faster than a large one.

The three way cats can oxidize hydrocarbons, convert CO into CO2, and remove NOx. Older type two way couldn't control NOx and so other systems had to be added to reduce that including EGR. EGR is still used, and I have read it's now used to control the temperature of the cat(s) to prevent melting them.
I purchased an aftermarket "performance" three way cat for a 1993 Mazda RX-7. As I recall, it used zirconium to attack the NOx, and other catalysts to handle the CO and hydrocarbons, all embedded on a strip of stainless steel, rolled into a spiral and stuffed into a stainless tube. It worked amazingly well considering the system I ended up with had no closed loop control. I often wondered how close I came to melting it!

Just to complicate the issue even more, we have the exhaust heat recovery device in there as well. It must be fun for the engineers to figure out this system!

And yes, "ceremony" is a poor translation of "procedure" or perhaps "system" as in the way it's done.