You have the concept right but the operation backward. The heated element of the O2 sensor (not O) will produce a small voltage in the absence of oxygen. The greater the oxygen content, the lower the voltage. 0.9 is about maximum output so not likely you'd see that amplitude in normal operation. 0.25-0.75 is closer to normal. The magic number that the voltage has to rise and fall against is 0.45v. That is the voltage corresponding to the ideal fuel mixture of 14.7:1 (by mass) - a condition somtimes marked by the Greek letter Lambda.

The feedback (closed-loop) emission control system does not work by trying to keep the fuel mixture at exactly 14.7:1 because of the needs of the catalytic converter.

The catalytic converter does multiple duty using multiple elements:
it requires a slight excess of oxygen for some reactions (oxidation) which allows the platinum and palladium to convert unburned hydrocarbons (HC) and carbon monoxide (CO) into carbon DIoxide (CO2) and water (H2O) AND,
it requires excess carbon dioxide (CO2) and a shortage of O2, to allow the rhodium catlyst to reduce oxides of nitrogen (NOx) into nitrogen (N) and carbon dioxide (CO2). In short, it needs two conflicting conditions.

To allow the converter to do all its jobs efficiently, the fuel mixture must constantly and quickly switch between slightly lean and slightly rich conditions. A properly operating sensor will cycle in less than one second. 12-14 times in 10 seconds is considered normal, 8 times is minimum. When a sensor gets contaminated and sluggish (cycle time takes longer), the result is usually too much time in "lean" mode causing insufficient reduction of NOx.

This is why NOx testing failures are so often cured by replacement of the O2 sensor and no other repairs.

The terminology; O2 is the form oxygen presents itself in earth's atmosphere. Oxygen always want to bond to something so "O" alone is unstable. O3 is more commonly called ozone.