why NO support for NUCLEO 410RB (1 can NOT program it in Arduino IDE) - but it present as Generic board?

[qq99]

problem is that MCU pin mapping to the BOARD pins in NUCLEO is different from Generic boards, so even Blink does not work.

No. Pin mapping is just a way to sort pins in a dedicated order. As stated you have to set the good LED pin in the example simply replace LED_BUILTIN in the blind example by the correct pin PYn.

Could you make new VARIANT for NUCLEO F410RB?

Because all this manual pin mapping is just a brainf*ck.
I (and all other people who have NUCLEO F410RB) can not change ARDUINO pins (i.e. D1, D2, A3, A4)
each time in the existing source code from other examples to original STM's pins such as PA1, PB3, PC5

As I already said - I'm not a programmer, I'm engineer who designing a hardware side and for testing purposes
use ready-to-use code examples, so I don't know how to write such complex stuff as new variant for the board.

[ag123]

use the generic variant, the pins are direct mapped, no changes are needed

[qq99]

use the generic variant, the pins are direct mapped, no changes are needed

read again what i wrote here on page-1 : Generic NOT works

you can try it by yourself with ANY nucleo board

[fpiSTM]

@qq99

I was able to get a Nucleo F410RB and it works as expected with the generic F410RB variant.
LED is on pin PA5 so the sketch is (simply replace LED_BUILTIN by PA5 in the Blink.ino):

void setup() {
// initialize digital pin LED_BUILTIN as an output.
pinMode(PA5, OUTPUT);
}

// the loop function runs over and over again forever
void loop() {
digitalWrite(PA5, HIGH); // turn the LED on (HIGH is the voltage level)
delay(1000); // wait for a second
digitalWrite(PA5, LOW); // turn the LED off by making the voltage LOW
delay(1000); // wait for a second
}

Upload method SWD which use STM32CubeProgrammer. It has to be installed manually on your PC, see the Wiki upload method section).