In Belgium, we have several different regions ( Flemish, Brussels and Wallonia)

For some integrations with Wallonia, we are currently forced to use the federal integration, since their implementation hasn't even started yet :(

You are correct about eidas, it seems to be handled by the federal government currently, but there's not much documentation on it ( Belgium) and i have seen some applications integrating that way. So i suppose the issue is documentation and discoverability.

And the partial conflict of interest with itsme

Belgium with its four governments is quite a weird edge case on many aspects of international standardisation. I don't don't much about the Belgian systems other than that there are several, but theoretical Belgium could make four systems work separately to authenticate abroad with the right federal setup.

Like is the case with my own government, I don't have very great expectations of Belgium's federal government and their IT projects. I'd wish countries could just share their implementations with other governments. Hell, I believe any code developed with public money should be open source for the benefit of everyone, but governments aren't a fan of that because companies charge more for developing software in the open.

Some source code of the Flemish government can be found on GitHub fyi