Will an Arduino UNO operating at 16mHz communicate with UART / I2C with an STM32 operating at a different frequency?
Tell me, does the difference in clock frequencies of microcontrollers affect the operation of buses between them?


No it doesn't. Or not much any way. It may affect the accuracy of clock generation1, which may have an affect at very high asynchronous baud rates, but other than that, no.

For synchronous communication it's all synchronised to the communication protocol's clock, so processor clocks are irrelevant.



1: Baud rates are usually generated as an integer division of the system clock. Different system clocks give different results for baud rate divisor calculations, yielding marginally different baud rates. Different baud rates will have different error percentages on different system clocks. At low speeds this has no noticeable affect. At high speeds (millions of bits per second) it can cause errors to creep in.