Install STM32CubeIDE on Raspberry PI

or maybe there is a utility for downloading firmware from Raspberry PI to STM 32

No.

At least not without some serious tinkering.

While most of it (including Eclipse) is written in Java, there are some components, e.g. the compiler itself, which are compiled to run on an Intel/AMD system.

Standalone CubeMX and CubeProgrammer might work though.

You can use st-flash ((sudo) apt-get install stlink-tools). There is also a gui alternative ((sudo) apt-get install stlink-gui). stlink-gui also install stlink-tools.

If you need a development tool chain, you can try binutils-arm-none-eabi. ((sudo apt-get install binutils-arm-none-eabi).

Best Regards.