At what depth of tread of my car tyres should I replace them? I have driven 38.450 km (23.890 miles) with them so far, mostly in city...?

In the UK our legal limit is 1.6 mm. I always replace at around 4 mm as I like to avoid accidents in the wet.

Mileage doesn’t matter. Tyre west  depends on many things, how powerful the car, FWD/RWD/AWD, how you drive. Driven carefully rear tyres on a FWD car can last 50 000 miles , if you did a track day in a high performance car, a few hundred.

Age is also important , as UV degrades the rubber over time esp the sidewalls. 7 years is probably the limit regardless of tread left.

In the UK , the minimum legal tread is 1.6 mm, but all government cars have the tyres replaced at 3mm, so I would regard that as the safe minimum.

Damage to sidewalks especially exposed cords, should also be a cause for replacement regardless of tread.

That depends on tyre condition. Mileage isn't everything. As Barry says, here in the UK the legal minimum of tread is 1.6mm over the centre 3/4 of the tread. That's ludicrously low and I too won't go below 4mm overall in our usually wet climate.  You need, too, to consider the rest of the tyre, if it's aging and cracking it's time for it to go.

U.S. law allows tires to be used until the tread has worn down to the minimum legal limit of 2/32 of an inch. 

If you drive in predominantly warm and dry areas, you could stretch tire usage to 2/32". 

But if you have regular rain or snow in the winter, I'd recommend changing the tires at 4/32".

The penny was good for something.  If you got one, stick it in the tire tread groove and if the tread touches or goes over Lincoln's hair then you got enough tread.  If the tread does not touch  the hair, your tire is BALD.  Basically 1/32 deep.

I LOVE GREEN TIRES! This means FUEL EFFICIENT ONES! MICHELIN made the HARMONY TIRE ((I think it was updated to another name) They came with an 80,000 mile warranty! SO I never bothered to check the treads. There are OTHER GREEN tires as well like CONTINENTAL< BRIDGESTONE and YOKOHAMA tires! They SAVE ON GAS and the sidewalls are made from a different type of COMPOUND < so they are QUIET and SMOOTHE and FORGIVING, and FLEXIBLE on bad roads. 23,000 miles is NOT very much! There is such a thing as a WEAR RATING for tires! The LARGER the number the LONGER they will last. MOST tires go at LEAST double 24,000 miles before they wear down! CHECK your ALIGNMENT and tell us WHAT type of car this is!   

If you live in areas where snow is possible, I suggest not letting tread get less than 1/8 inch.