Cross Compiling for Arm cortex M0 Pi Pico RP2040

hi,
I am trying to cross-compile for Raspberry Pi Pico (RP2040 in my case it is a Cortex M0+) and I noticed some contributors made great contributions to the Toolchain for arm development.
Namely https://build.opensuse.org/project/show/home:wkazubski
and also
https://build.opensuse.org/project/show/home:duwe:crosstools2

So I installed both toolchains and the problem I have is that none of those can compile the pico-examples.
crosstools2 does not have includes for c++ so the compile fails.

And Wojciech Kazubski compiler is not recognized by the cmake generated makefiles …
I always get and error saying make can not find a compiler.
Both in the /usr/arm-none-eabi/ directory or on
/opt/cross/.

Does anyone tried to make a cross compile ?
Pi Pico is a very popular platform and I can use Virtualbox to run other distro and work there.
But that is really not a good thing.
Anyone has an idea about how to make the cross-compiler work ?

Regards,