Small AC wall warts (transformers) tend to have a much higher output voltage under no or a light load. Your 12Vac adapter could easily output 16Vac, and when you rectify that you have around 16 * sqrt(2) = 22.6Vdc Corrected for 2 diode drops of the bridge 21.4V left.
So if the caps are rated for 35V you have plenty of headroom there.
Another concern is the temperature of your voltage regulators.
These will produce more heat when being fed with a higher voltage.
They do not have much cooling (just the a(aluminimum?) standoff nut ?) but they likely also do not have to deliver much current.
If the voltage regulators get overheated, they lower the current / output voltage.
This means that the circuit wont function properly anymore, but it's unlikely anything will get damaged permanently.
You could run it for a while and then check the temperature of the voltage regulators.
As a rule of thumb if you put a wet finger to it and it doesn't sizzle then it's probably OK, but most prefer to keep their electonics under 70Celcius.
Some other things to check, (Even if jus to get more experience with datasheets)
Get the datasheets of your voltage regulators (Same ST brand, datasheets from other manufacturers may vary) and check the maximum input voltages.
For the 7815 It's probably 35V, but for the 5V regulators it's probably lower, but they are also likely to be fed from the output of the 15V regulators.
U14 is probably also an voltage regulator (AMD1117-3V3?)