And annother controller with a slow SPI library as provided by the manufacturer

[RudolphRiedel]

Anyone who can guess what controller this is?

This is running under Arduino, no special treatment for the controller in place, just the SPI class SPI.transfer() plus digitalWrite().
The Arduino core is supplied by the manufacturer of the controller.
The SPI clock is 8MHz so transferring a byte is done in 1µs but the library needs >4µs before and after the transfer of each byte.
This is a 32 bit single-core controller running at 32MHz.