[Integrator] Move/Create methods into integrator.common

[EdgarGF93]

I will move some things from azimuthal integrator to common, that i need for Fiber, so I wont copy code

[kif]

Partially implemented in #2786. This PR is merged in a bugfix release (2026.02) but the work in not yet completed.
Several new methods in the PR are missing decent docstrings.