Is SPI thread safe?

I need to use same SPI port (MOSI, MISO, SCK) with different Chip Select (CS). However [SPI class](https://github.com/arduino/ArduinoCore-mbed/blob/bbc628439eb4dd64b70348e91ecda8e0c45e318c/libraries/SPI/SPI.h#L31) is not supporting CS. Therefore I need to code like:
```
#include "SPI.h"
#include "mbed.h"

rtos::Thread thread;

auto CS0 = D7;
auto CS1 = D6;

void thread_func() {
digitalWrite(CS0, LOW);
SPI.begin();
digitalWrite(CS0, HIGH);
}

void setup() {
pinMode(CS0, OUTPUT);
digitalWrite(CS0, HIGH);
pinMode(CS1, OUTPUT);
digitalWrite(CS1, HIGH);

thread.start(mbed::callback(thread_func));

digitalWrite(CS1, LOW);
SPI.begin();
digitalWrite(CS1, HIGH);
}

void loop() {}
```
Is this thread safe? Is there any chance CS0 and CS1 to go LOW at the same time?

On the other hand, mbed's SPI supports CS pin.

If Arduino's SPI is not thread safe, how about using mbed's SPI CS pin?

The relevant entry points are libraries/SPI/SPI.h and cores/arduino/mbed/drivers/include/drivers/SPIMaster.h; compare their chip-select and synchronization behavior and reproduce the two-thread example on a supported board. Done means documenting whether Arduino SPI and mbed SPI with CS are safe for this use, including any limitations.

Written by the indexing model from the issue text.