Run doctest and linkcheck again

[jl-wynen]

The new pixi setup only builds the docs but does not test them like we used to. We should run doctest and linkcheck in our CI.

[jl-wynen]

#601 implements the doctest part of this. We used to run linkcheck only on main because it can be flaky and we didn't want to block PRs. But we no longer run the pipeline on main. How can we best do this?