Adaptive mesh refinement API

In https://github.com/Ferrite-FEM/Ferrite.jl/pull/780 Maxi develops the main infrastructure for "p4est-type" AMR~1 (which we currently name BGW internally, derived from the author names). In addition I am planning to implement "multilevel-type" AMR [2]. This raises the question how an API might look like for using these meshes efficiently and which key components can be reused. Specifically
1. Can we work directly on the mesh representations and get away with a single dof handler by being clever with the dispatches?
2. How does the interaction with constraint handler look like?
3. How can we efficiently reuse our FEValues? I.e. reinit for multilevel type meshes work similar as reinit for Nedelec elements (i.e. need a pre-processing step of the basis functions)
4. How to transport solution vectors between consecutive AMR steps?
5. Whch components can be reused between AMR implementations (e.g. balancing?)
6. How to iterate and integrate over faces (see https://github.com/Ferrite-FEM/Ferrite.jl/pull/743#discussion_r1253414316)

# References

1. Burstedde, Carsten, Lucas C. Wilcox, and Omar Ghattas. "p4est: Scalable algorithms for parallel adaptive mesh refinement on forests of octrees." SIAM Journal on Scientific Computing 33.3 (2011): 1103-1133.
7. Zander, Nils, et al. "Multi-level hp-adaptivity: high-order mesh adaptivity without the difficulties of constraining hanging nodes." Computational Mechanics 55.3 (2015): 499-517.