Given a lot of Arduino these days have mbed or freertos under the covers, with some way to expose it, that may have been a better route for the author's style.
Zephyr is easy to use (Clion also has good support for it), but like, you can't just choose not to install the toolchain and expect it to all work.
It also definitely supports the Pi Pico - i've used it on it before, no issues.
A simpler rundown of these RTOSen would be:
1. FreeRTOS - supported by roughly everything, but drivers and such are mostly per-SOC/device, which is a pain in the ass. The APIs are not very user friendly, but you get used to it.
To give a sense of level - if you wanted to use bluetooth with FreeRTOS, you get to find your own stack.
2. Zephyr - supports real hardware abstractions and supports most SOC. You may have to do a little board work.
If you wanted to use bluetooth with Zephyr, it has a bluetooth stack you can use, you may have to add a little support for your HCI.
3. NuttX - not great support, but very cool if you can get it working - not really highly supported by industry yet.
I never got far enough into NuttX to try bluetooth in NuttX.
There is also mbed, but we'll skip it.
In practice, people in the RTOS world will usually go with what the SOC vendor supports. So if you are using Nordic stuff, you are probably on Zephyr. If you are using NXP stuff, probably FreeRTOS, etc.
That is how they get good support.